Question 1 :
If $3$ coins are tossed simultaneously, the probability of $1$ head and $2$ tails is:
Question 2 :
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 3 :
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 4 :
A coin is tossed. What is the probability of getting a head and a tail?
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 :
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 7 :
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 8 :
The probability that a leap year will have only $52$ Sundays is
Question 9 :
Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. Theprobability of drawing two aces is.<br>
Question 10 :
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 11 :
Find probability of bag chosen out random contains more than 5 kg.
Question 12 :
A coin is tossed $5$ times. The probability of $2$ heads and $3$ tails is:
Question 13 : <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 14 : <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 15 :
In a non-leap year the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is.
Question 16 :
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 17 :
If a coin is tossed, then the probability that a head turns up is ______.
Question 18 : <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 19 :
What is the probability that there are $5$ Mondays in the month of February 2016?
Question 20 :
When two dice are thrown simultaneously the probability that the sum of the two numbers that turn up is more than $11$ is:
Question 21 :
A die is thrown once. The probability of getting a number $3$ or $4$ is _________.
Question 22 :
A coin is tossed five times, find the probability of getting no head.
Question 23 :
When $2$ dice are thrown simultaneously what is the probability that there is exactly one $5$?
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 : 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 26 :
Assertion: Consider an event for which probability of success is 1/2.<br>Probability that in n trials,there are r success where r-4K and k is an integer is $\dfrac{1}{4}+\dfrac{1}{2^{n/2+1}}cos (\dfrac{n\pi}{4})$
Reason: $^nC_0+^nC_4+^nC_7+.......=2^{n/2} sin (\dfrac{n \pi}{4})$
Question 27 :
When two dice are thrown simultaneously, the probability that the sum of the two numbers that turn up is less than $11$ is:
Question 28 :
From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.
Question 29 : <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 30 :
What is the probability that a two digit number selected at random will be a multiple of $3$ and not a multiple of $5$?
Question 31 :
What is the total number of candidates at an examination, if 31 % fail and the number of failing students is 248.
Question 32 :
In a World Cup final match against Srilanka, for six times Sachin Tendulkar hits a six out of $30$ balls he plays. What is the probability that in a given throw the ball does not hit a six?
Question 33 :
A bag contains $14$ balls of two colours, the number of balls of colour being equal, seven balls are drawn at random one by one. The ball in hand is returned to the bag before each new draw. The probability that at least $3$ balls of each colour are drawn, is:
Question 35 :
Let ${ S }_{ n }=\displaystyle\sum _{ k=1 }^{ n }{ k }$ denote the sum of the first $n$ positive integers. The numbers ${ S }_{ 1 }, { S }_{ 2 }, { S }_{ 3 }, \dots , { S }_{ 99 }$ are written on $99$ cards. The probability of drawing a card with an even number written on it is
Question 36 : <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 37 :
In a single throw of two dice, find the probability that neither a doublet nor a total of 8 will appear.<br>
Question 38 :
A box contains $40$ red and blue marbles. If a marble is drawn at random, the probability of picking a blue marble is $\dfrac {3}{8}$. Ansh takes out one red and nine blue marbles and then draws a marble at random. Find the probability of drawing a blue marble
Question 39 : <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 40 :
$60$ percent people in a group of $10$ people, have brown eyes. Two people are to be selected at random from the group. What is the probability that <u>neither</u> person selected will have brown eyes?
Question 41 :
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 42 : 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 43 :
An urn contains one black ball and one green ball. A second urn contains one white and one green ball. One ball is drawn at random from each urn. What is the probability that both balls are of same colour?
Question 44 :
A couple of dice rolled. What is the empirical probability of getting the sum as $5$?<br/>
Question 45 :
A die is rolled so that the probability of face $i$ is proportional to $i,\,\,\{i=1,2,.....6\}$. The probability of an even number occurring when the die is rolled, is
Question 46 :
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 47 :
Set $S$ has $4$ elements, $A$ and $B$ are subsets of $S$. The probability that$A$ and $B$ are not disjoint is
Question 48 :
A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is
Question 49 :
A bag contains $15$ red, $8$ blue and several green marbles. A marble is selected at random. The probability of drawing a blue marble is $\dfrac {1}{5}$. $5$ green marbles are now taken out from the bag. If a marble is now drawn at random, find the probability of drawing a green marble
Question 50 :
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 51 :
In a school, $\displaystyle \frac{5}{8}$ of the total students are girls. If the number of girls is $120$ more than that of the boys. What is the strength of the school? how many boys are there?
Question 52 :
A box contains coupons labeled 1, 2, 3, ... , n. A coupon is picked at random and the number x is noted. The coupon is put back into box and a new coupon is picked at random. The new number is y. Then the probability that one of the numbers x, y divides the other is : (in the options below [r] denotes the largest integer less than or equal to r)
Question 53 :
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?
Question 54 :
A dies is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $5$ is:
Question 55 :
A die is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $6$ is:
