Question 1 :
In a shooting game, John shoots the balls $20$ times out of $40$ trials. What is the empirical probability of the shooting event?<br/>
Question 2 : There are $40$ students in a class and their results is presented as below :<table class="wysiwyg-table"><tbody><tr><td>Result (Pass/Fail)</td><td>Pass</td><td>Fail</td></tr><tr><td>Number of Students</td><td>$30$</td><td>$10$</td></tr></tbody></table><p></p> If a student chosen at random out of the class, find the probability that the student has passed the examination<br/>
Question 3 : <p>There are $40$ students in a class and their results is presented as below :</p><table class="wysiwyg-table"><tbody><tr><td>Result (Pass/Fail)</td><td>Pass</td><td>Fail</td></tr><tr><td>Number of Students</td><td>$30$</td><td>$10$</td></tr></tbody></table><p></p><p>If a student chosen at random out of the class, find the probability that the student has passed the examination.</p>
Question 4 :
What is the probability that there are $5$ Mondays in the month of February 2016?
Question 5 :
A die is tossed $80$ times and the number $3$ is obtained $14$ times. Now, a dice is tossed at random, then the probability of getting the number $3$ is ________.
Question 6 : <p>$400$ students of class $X$ of a school appeared in a test of $100$ marks in the subject of social<br/>studies and the data about the marks secured is as below :<span class="wysiwyg-font-size-medium"><br/></span></p><span class="wysiwyg-font-size-medium"></span><table class="wysiwyg-table"><tbody><tr><td><span> Marks <br/> secured</span></td><td><span>Number of <br/></span>Students</td></tr><tr><td> $0-25$</td><td> $50$</td></tr><tr><td> $26-50$</td><td> $220$</td></tr><tr><td> $51-75$</td><td> $100$</td></tr><tr><td> Above $75$</td><td> $30$</td></tr><tr><td>Total number of students</td><td> $400$</td></tr></tbody></table><p><span class="wysiwyg-font-size-medium"></span></p><p><span class="wysiwyg-font-size-medium"></span></p><p><span class="wysiwyg-font-size-medium"></span></p><p></p><span class="wysiwyg-font-size-medium"></span><p>If the result card of a student he picked up at random, what is the probability that the student has secured more than $50$ marks.</p>
Question 7 :
When a coin is tossed at random, then the probability of getting a head is ________.
Question 8 : <p>A coin is tossed $150$ times and the outcomes are recorded. The frequency distribution of the outcomes $H$ (i.e, head) and $T$ (i.e, tail) is given below :</p><table class="wysiwyg-table"><tbody><tr><td>Outcome</td><td>$H$</td><td>$T$</td></tr><tr><td>Frequency</td><td>$85$</td><td>$65$</td></tr></tbody></table><p><span class="wysiwyg-font-size-medium"></span></p><p>Find the value of $P(H)$, i.e, probability of getting a head in a single trial.</p>
Question 9 : A die is thrown $200$ times and the outcomes $1, 2, 3, 4, 5, 6$ have frequencies as below:<span class="wysiwyg-font-size-medium"> </span><span class="wysiwyg-font-size-medium"><br/></span><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p><span class="wysiwyg-font-size-medium">Outcome</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$1$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$2$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$3$</span><span class="wysiwyg-font-size-medium"><br/> </span></p></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$4$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$5$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$6$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p><span class="wysiwyg-font-size-medium">Frequency</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$40$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$38$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$43$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$29$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$28$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$22$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr></tbody></table><p><span class="wysiwyg-font-size-medium"><span>Find the probabilities of </span><span>getting a number more than $1$ and less than $6$ </span><span>in a toss (trial).</span><br/></span></p>
Question 10 :
In a single throw of a die, the probability of getting a multiple of $3$ is ____________.
Question 11 :
Two men hit at a target with probabilities <span>$\dfrac{1}{2}$</span> and <span>$\dfrac{1}{3}$ </span>respectively. What is the probability that exactly one of them hits the target?
Question 12 : <p>There are $500$ packets in a large box and each packet contains $4$ electronic devices in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as below:</p><table class="wysiwyg-table"><tbody><tr><td><span>No. of faulty <br/></span>devices in a packet</td><td>Number of packets</td></tr><tr><td> $0$</td><td> $300$</td></tr><tr><td> $1$</td><td> $100$</td></tr><tr><td> $2$</td><td> $50$</td></tr><tr><td> $3$</td><td> $30$</td></tr><tr><td> $4$</td><td> $20$</td></tr><tr><td>Total number of packets</td><td> $500$</td></tr></tbody></table><p>If one packet is drawn from the box, what is the probability that all the four devices in the packet are without any fault?</p>
Question 13 : A die having six faces is tossed $80$ times and the data is as below:<span class="wysiwyg-font-size-medium"> </span><span class="wysiwyg-font-size-medium"><br/></span><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p>Outcome</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$1$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$2$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$3$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$4$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p>$5$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$6$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p>Frequency</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$10$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$20$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$10$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$28$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$8$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$4$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr></tbody></table><p>Find $P (1) $.</p>
Question 14 : <p>A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table show the result of $1000$ cases :</p><table class="wysiwyg-table"><tbody><tr><td>Distance in $Km$</td><td>Frequency</td></tr><tr><td>Less than $4000$</td><td> $20$</td></tr><tr><td>$4000$ to $9000$</td><td> $210$</td></tr><tr><td>$9000$ to $14000$</td><td> $325$</td></tr><tr><td>More than $14000$</td><td> $445$</td></tr></tbody></table><p><span>If you buy a tyre of this company what is the probability that it</span><span> will need to be replaced after it has covered somewhere between $4000\, km$ and $14000\, km$?</span></p>
Question 15 :
When two dice are thrown simultaneously, the probability that the sum of the two numbers that turn up is less than $11$ is:
Question 16 : A survey was conducted by car manufacturing company in a metropolitan city on $1000$ persons having monthly income from Rs. $30,001$ to Rs. $50,000$. The data about the number of persons in various categories is as under:<span class="wysiwyg-font-size-medium"><br/></span><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">Monthly income</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td colspan="3"><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">Number of Cars</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">(in rupees)</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$1$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$2$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">More than $2$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$30,001-40,000$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$400$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$50$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$25$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$40,001-50,000$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$100$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$300$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$125$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr></tbody></table><span> </span><span>Find the probability that a person selected at random i</span><span>n the income slab $40,001-50,000$ have more than $2$ cars.</span>
Question 17 : <p>A coin is tossed $150$ times and the outcomes are recorded. The frequency distribution of the outcomes $H$ (i.e., head) and $T$ (i.e., tail) is given below :</p><table class="wysiwyg-table"><tbody><tr><td>Outcome</td><td>$H$</td><td>$T$</td></tr><tr><td>Frequency</td><td>$85$</td><td>$65$</td></tr></tbody></table><p></p><p>Find the value of $P(H)$, i.e., probability of getting a head in a single trial.</p>
Question 18 : <p>Fifty seeds were selected at random from each of $5$ bags $A, B, C, D, E$ of seeds, and were kept under standardised conditions equally favourable to germination. After $20$ days, the number of seeds which had germinated in each collection were counted and recorded as follow :</p><span class="wysiwyg-font-size-medium"></span><table class="wysiwyg-table"><tbody><tr><td>Bag</td><td>$A$</td><td>$B$</td><td>$C$</td><td>$D$</td><td>$E$</td></tr><tr><td><p>Number of seeds</p><p> germinated</p></td><td>$40$</td><td>$48$</td><td>$42$</td><td>$39$</td><td>$41$</td></tr></tbody></table><p><span class="wysiwyg-font-size-medium"></span></p><p><span class="wysiwyg-font-size-medium"></span></p><p></p><span class="wysiwyg-font-size-medium"></span><p>What is the probability of germination of</p><p>$(i)$ more than $40$ seeds in a bag?</p><p>$(ii)$ $49$ seeds in a bag?</p><p>$(iii)$ more than $35$ seeds in a bag?</p><p><br></p>
Question 19 :
In a single throw of two dice, find the probability that neither a doublet nor a total of 8 will appear.<br>
Question 20 :
A box contains $32$ coloured marbles. $8$ of them are red marbles and the rest are either blue or green marbles. A marble is drawn at random. Calculate the probability of drawing a marble which is not red in colour.
Question 21 :
A bag contains 100 tickets bearing numbers 1-100. A ticked is taken out randomly, find the probability of getting a ticket bearing a number which is the multiple of 25.
Question 22 :
A bag contains a number of marbles of which $80$ are red, $24$ are white and the rest are blue. If the probability of randomly selecting a blue marble from this bag is $\dfrac {1}{5}$, how many blue marbles are there in the bag?
Question 23 :
In a non-leap year the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is.
Question 24 : On one page of a telephone directory there were $200$ telephone numbers. The frequency distribution of their unit place digit is given in the following table:<table class="wysiwyg-table"><tbody><tr><td>Digit</td><td>$0$</td><td>$1$</td><td>$2$</td><td>$3$</td><td>$4$</td><td>$5$</td><td>$6$</td><td>$7$</td><td>$8$</td><td>$9$</td></tr><tr><td>Frequency</td><td>$22$</td><td>$26$</td><td>$22$</td><td>$22$</td><td>$20$</td><td>$10$</td><td>$14$</td><td>$28$</td><td>$16$</td><td>$20$</td></tr></tbody></table>
Question 25 :
A die is thrown once. The probability of getting a number $3$ or $4$ is _________.
Question 26 : A die is thrown $400$ times, the frequency of the outcomes of the events are given as under.<br/><table class="wysiwyg-table"><tbody><tr><td>outcome<br/></td><td>$1$<br/></td><td>$2$<br/></td><td>$3$<br/></td><td>$4$<br/></td><td>$5$<br/></td><td>$6$<br/></td></tr><tr><td>Frequency<br/></td><td>$70$<br/></td><td>$65$<br/></td><td>$60$<br/></td><td>$75$<br/></td><td>$63$<br/></td><td>$67$<br/></td></tr></tbody></table>Find the probability of occurrence of an odd number.<br/>
Question 27 :
A couple of dice rolled. What is the empirical probability of getting the sum as $5$?<br/>
Question 28 :
A pair of dies is thrown, find the probability of getting a total of numbers is more than $10$.
Question 30 : Observe the table given.<table class="wysiwyg-table"><tbody><tr><td>Club</td><td>English</td><td>Maths</td><td>Science</td></tr><tr><td>Number of students</td><td>$99$</td><td>$121$</td><td>$154$</td></tr></tbody></table>A student is chosen randomly from the group as the co-ordinator of all the clubs. What is the probability that the student is from the science club?
Question 31 :
A card is drawn from a well-shuffled deck of playing cards. Find the probability of drawing a face card.
Question 32 : To know the opinion of the student about the subject<span class="wysiwyg-font-size-medium"> </span>statistic, a survey of $200$ students was conducted.<p>The data is recorded in the following table</p><table class="wysiwyg-table"><tbody><tr><td>Opinion</td><td>Like</td><td>Dislike</td></tr><tr><td>No. of Students</td><td>$135$</td><td>$65$</td></tr></tbody></table><p>Find the probability that a student chosen at random</p><span class="wysiwyg-font-size-medium"></span><p></p><p></p><p></p><p>$(i)$ likes statistics, $(ii)$ does not like it.</p>
Question 33 :
When two dice are thrown simultaneously the probability that the sum of the two numbers that turn up is more than $11$ is:
Question 34 : <p>There are $500$ packets in a large box and each packet contains $4$ electronic devices in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as below :</p><table class="wysiwyg-table"><tbody><tr><td>No. of faulty devices in a packet</td><td>Number of packets</td></tr><tr><td> $0$</td><td> $300$</td></tr><tr><td> $1$</td><td> $100$</td></tr><tr><td> $2$</td><td> $50$</td></tr><tr><td> $3$</td><td> $30$</td></tr><tr><td> $4$</td><td> $20$ </td></tr><tr><td>Total number of packets</td><td> $500$ </td></tr></tbody></table><p>If one packet is drawn from the box, what is the probability that all the four devices in the packet are without any fault?</p>
Question 35 :
A box has tokens numbered $3$ to $100$. If a token is taken out at random the chance that the number is divisible by $7$ is
Question 36 : <p>The record of a weather station shows that out of the past $250$ consecutive days, its weather forecasts were correct $175$ times.<span> What is the probability that on a given day it was correct?</span></p>
Question 37 :
A ball is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles. The probability of a ball drawn is red, white or blue .......
Question 38 :
A card is drawn at random from a pack of well shuffled $52$ cards. What is the probability of getting a queen of red suit?
Question 39 :
From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.
Question 40 :
The probability that a two digit number selected at random will be a multiple of '$3$' and not a multiple of '$5$' is<br/>
Question 41 :
In a survey of $364$ children aged $19-36$ months, it was found that $91$ liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is :<br>
Question 42 :
A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting a club card?
Question 43 :
Bag contains $100$ tickets bearing numbers $1-100$. A ticket is taken out randomly, find the probability getting of a even numbered ticket.<br/>
Question 44 : Two coins are tossed $1000$ times and the outcomes are recorded as below:<br/><table class="wysiwyg-table"><tbody><tr><td>No of heads<br/></td><td>$2$<br/></td><td>$1$<br/></td><td>$0$<br/></td></tr><tr><td>Frequency<br/></td><td>$200$<br/></td><td>$550$<br/></td><td>$250$<br/></td></tr></tbody></table>Based on this information, the probability for at most one head is $\dfrac{a}{b}$, where $(a,b)=1$. Then $\dfrac{a}{b}$ is<br/>
