Question 1 :
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 2 :
Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. Theprobability of drawing two aces is.<br>
Question 3 : <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"><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 ofseeds</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"></p><p><span class="wysiwyg-font-size-medium"></p><p></p><span class="wysiwyg-font-size-medium"><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 4 :
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 5 :
Two men hit at a target with probabilities $\dfrac{1}{2}$ and $\dfrac{1}{3}$ respectively. What is the probability that exactly one of them hits the target?
Question 6 :
In a box containing only purple and green marshmallows, $6$ marshmallows are purple. If the probability of choosing a purple marshmallow from the box is $\dfrac {1}{3}$, calculate the number of green marshmallows in the box.
Question 7 :
If a coin is tossed, then the probability that a head turns up is ______.
Question 8 : <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 <br/>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 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 class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p><span class="wysiwyg-font-size-medium">Outcome</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$1$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$2$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$3$<span class="wysiwyg-font-size-medium"><br/>  </p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$4$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$5$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$6$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p><span class="wysiwyg-font-size-medium">Frequency</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$40$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$38$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$43$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$29$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$28$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$22$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr></tbody></table><p><span class="wysiwyg-font-size-medium">Find the probabilities of getting a number more than $1$ and less than $6$ in a toss (trial).<br/></p>
Question 10 :
If $3$ coins are tossed simultaneously, the probability of $2$ heads and $1$ tail is:
Question 11 :
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 12 :
A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting a club card?
Question 13 :
Find probability of bag chosen out random contains more than 5 kg.
Question 14 :
If a coin is tossed twice, find the probability of getting at least one head.
Question 15 :
The probability that a leap year will have only $52$ Sundays is
Question 16 :
If $A,B$ be two events such that $P(A\cup B)=\dfrac{5}{6}$, $P(A\cap B)=\dfrac{1}{3}$ and $P(B')=\dfrac{1}{2}$, then events $A,B$ are
Question 17 :
A coin is tossed. What is the probability of getting a head and a tail?
Question 18 :
If $3$ coins are tossed simultaneously, the probability of $1$ head and $2$ tails is:
Question 19 :
In a single throw of a die, the probability of getting a multiple of $3$ is ____________.
Question 20 :
A coin is tossed five times, find the probability of getting no head.
Question 21 : 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 22 :
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 24 : To know the opinion of the student about the subject<span class="wysiwyg-font-size-medium"> 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"><p></p><p></p><p></p><p>$(i)$ likes statistics, $(ii)$ does not like it.</p>
Question 25 :
When two dice are thrown simultaneously the probability that the sum of the two numbers that turn up is more than $11$ is:
Question 26 : <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"></p><p>Find the value of $P(H)$, i.e, probability of getting a head in a single trial.</p>
Question 27 :
The probability for a randomly chosen month to have its $10^{th}$ day as Sunday, is.
Question 28 : A die having six faces is tossed $80$ times and the data is as below:<span class="wysiwyg-font-size-medium"> <span class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p>Outcome</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$1$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$2$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$3$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$4$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p>$5$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$6$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p>Frequency</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$10$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$20$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$10$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$28$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$8$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$4$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr></tbody></table><p>Find $P (1) $.</p>
Question 29 : 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 30 :
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 31 :
What is the probability that there are $5$ Mondays in the month of February 2016?
Question 32 : <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 33 : 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/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">Monthly income</p><span class="wysiwyg-font-size-medium"><br/> </td><td colspan="3"><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Number of Cars</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">(in rupees)</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$1$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$2$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">More than $2$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$30,001-40,000$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$400$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$50$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$25$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$40,001-50,000$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$100$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$300$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$125$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr></tbody></table> Find the probability that a person selected at random in the income slab $40,001-50,000$ have more than $2$ cars.
Question 34 :
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 35 :
When $2$ dice are thrown simultaneously what is the probability that there is exactly one $5$?
Question 37 : <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/></p><span class="wysiwyg-font-size-medium"><table class="wysiwyg-table"><tbody><tr><td>            Marks <br/>           secured</td><td>Number of <br/>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"></p><p><span class="wysiwyg-font-size-medium"></p><p><span class="wysiwyg-font-size-medium"></p><p></p><span class="wysiwyg-font-size-medium"><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 38 :
A die is thrown once. The probability of getting a number $3$ or $4$ is _________.
Question 39 :
In a non-leap year the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is.
Question 40 : <p>The record of a weather station shows that out of the past $250$ consecutive days, its weather forecasts were correct $175$ times. What is the probability that on a given day it was correct?</p>
