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 : 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>&#160;Find the probability that a person selected at random in the income slab $40,001-50,000$ have more than $2$ cars.

Question 3 : 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 4 : If $3$ coins are tossed simultaneously, the probability of $1$ head and $2$ tails is:

Question 5 : 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 6 : <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>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$0$</td><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160;$300$</td></tr><tr><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$1$</td><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160;$100$</td></tr><tr><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$2$</td><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$50$</td></tr><tr><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$3$</td><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$30$</td></tr><tr><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$4$</td><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$20$</td></tr><tr><td>Total number of packets</td><td>&#160; &#160; &#160; &#160; &#160; &#160; &#160; $500$</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 7 : When two dice are thrown simultaneously the probability that the sum of the two numbers that turn up is more than $11$ is:

Question 8 : 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 9 : 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 11 : Set $S$ has $4$ elements, $A$ and $B$ are subsets of $S$. The probability that$A$ and $B$ are not disjoint is

Question 12 : <p>A&#160;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>&#160; &#160; &#160; &#160;$20$</td></tr><tr><td>$4000$ to $9000$</td><td>&#160; &#160; &#160; $210$</td></tr><tr><td>$9000$ to $14000$</td><td>&#160; &#160; &#160; $325$</td></tr><tr><td>More than $14000$</td><td>&#160; &#160; &#160; $445$</td></tr></tbody></table><p>If you buy a tyre of this company what is the probability that it&#160;will need to be replaced after it has covered somewhere between $4000\, km$ and $14000\, km$?</p>

Question 13 : 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 14 : What is the total number of candidates at an examination, if 31 % fail and the number of failing students is 248.

Question 15 : 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 16 : $60$ percent people in&#160;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 17 : A couple of dice rolled. What is the empirical probability of getting the sum as $5$?<br/>

Question 18 : In an examination, the probability of a candidate solving a question is&#160;$\dfrac{1}{2}$. Out of given $5$ questions in the examination, what is the probability that the candidate was able to solve at least $2$ questions?

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 : 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 21 : 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 22 : A die is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $6$ is:

Question 23 : A dies is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $5$ is:

Question 24 : 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 25 : 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 :&#160;(in the options below [r] denotes the largest integer less than or equal to r)