Question 1 : 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 2 :
In a non-leap year the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is.
Question 3 :
The probability for a randomly chosen month to have its $10^{th}$ day as Sunday, is.
Question 4 :
The probability that a leap year will have only $52$ Sundays is
Question 5 :
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 6 : 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 7 : <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>
Question 8 : 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 9 : <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 10 :
A coin is tossed $5$ times. The probability of $2$ heads and $3$ tails is:
Question 11 :
A coin is tossed five times, find the probability of getting no head.
Question 12 :
If $3$ coins are tossed simultaneously, the probability of $1$ head and $2$ tails is:
Question 13 : <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 14 :
If a coin is tossed, then the probability that a head turns up is ______.
Question 15 :
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 16 :
If $3$ coins are tossed simultaneously, the probability of $2$ heads and $1$ tail is:
Question 17 :
When two dice are thrown simultaneously the probability that the sum of the two numbers that turn up is more than $11$ is:
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"><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 19 :
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 20 :
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 21 :
If a coin is tossed twice, find the probability of getting at least one head.
Question 22 : 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 23 :
A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting a club card?
Question 24 :
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 25 :
A coin is tossed. What is the probability of getting a head and a tail?
Question 26 : 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<br>
Question 27 :
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 28 :
There are only two women among $20$ persons taking part in a pleasure trip. The $20$ persons are divided into two groups, each group consisting of $10$ persons. Then the probability that the two women will be in the same group is:
Question 29 :
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 30 : <p>Two dice are thrown. The number of sample points in the sample space when six does not appear on any one side is</p>
Question 31 :
From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.
Question 32 : 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 33 :
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 34 : <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>If you buy a tyre of this company what is the probability that it will need to be replaced after it has covered somewhere between $4000\, km$ and $14000\, km$?</p>
Question 35 :
What is the total number of candidates at an examination, if 31 % fail and the number of failing students is 248.
Question 36 :
Archaeological survey indicates that the odd of occurring earthquake in Greater Himalayan region due to Tehri Dam are $5$ to $7$. What is the probability of earthquake in Greater Himalayan region?
