Question 1 : One percent of the population suffers from a certain disease. There is blood test for this disease, and it is $99\%$ accurate, in other words, the probability that is gives the correct answer is $0.99$, regardless of whether the person is sick or healthy. A person takes the blood test, and the result says that he has the disease. The probability that he actually has the disease, is?

Question 2 : $10$ persons are seated around a round table. What is the probability that $4$ particular persons are always seated together?

Question 3 : If A and B are independent events,then  $P\left ( \dfrac{B}{A} \right )= $

Question 4 : If $P(A) + P(B) = 1$; then which of the following option explains the event $A$ and $B$ correctly ?

Question 5 : A bag contain $4$ white and $2$ black balls. Two balls are drawn at random. The probability that they are of the same colour is ________.

Question 6 : If A and B are two events such that $P\left ( A \right )> 0$ and $P\left ( B \right )\neq 1$, then $P\left ( \bar{A}/\bar{B} \right )= $

Question 7 : A four-digit number is formed by using the digits 1, 2, 4, 8 and 9 without repitition. If one number is selected from those numbers, then what is the probability that it will be an odd number ?

Question 8 : $2n$ boys are randomly divided into two subgroups containing $n$ boys each. The probability that the two tallest boys are in different groups is

Question 9 : <p class="MsoNormal">If a fair die is rolled $4$ times, then what is the&#10;probability that there are at least $2$ sixes ?</p>

Question 10 : A bouquet from $11$ different flowers is to be made so that it contains not less then three flowers . Then the number of the different ways of selecting flowers to from the bouquet

Question 11 : <p class="MsoNormal">A box contains $10$ items, $3$ of which are defective.&#10;If $4$ are selected at random without replacement, what is the probability&#10;that at least $2$ of the $4$ are defective?</p>

Question 12 : If $5$ of a company's $10$ delivery trucks do not meet emission standard and $3$ of them are chosen for inspection, then what is the probability that none of the trucks chosen will meet emission standards ?

Question 13 : Of the students in a college, it is known that $60\%$ reside in hostel and $40\%$ are day scholars (not residing in hostel). Previous year results report that $30\%$ of all students who reside in hostel attain A grade and $20\%$ of day scholar attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostile?

Question 14 : Counters numbered $1,2,3$ are placed in a bag and one is drawn at random and replaced. The operation is being repeated three times. The probabolity of obtaining a total of $6$ is ?<br/>

Question 15 : A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or I, III or all the three. The probabilities of the student passing in tests I, II and III are m, n and $\dfrac{1}{2}$ respectively. If the probability of the student to be successful is $\dfrac{1}{2}$, then which one of the following is correct?

Question 16 : If $\overline { E } $ and $\overline { F } $ are the complementary events of events $E$ and $F$ respectively and if $0&lt;P(F)&lt;1$, then

Question 17 : A box contains $100$ tickets numbered $1,2,.....100$. Two tickets are chosen at random. It is given that the minimum number on the two chosen tickets is not more than $10$. The maximum number on them is $5$ with probability.<br>

Question 18 : If two events A and B are such that&#160;$P(A)=0.75\&#160; &#160;P(B|A)=0.8\ P(B|A')=0.6$ Find P(B)

Question 19 : If $P(A\cap B)=7/10$ and $P(B)=17/20$, where $P$ stands for probability then $P(A|B)$ is equal tp

Question 20 : <p>From a batch of $100$ items of which $20$ are defective, exactly two items are chosen, one at a time, without replacement. Calculate the probabilities that&#160;both items chosen are defective</p>

Question 21 : A box contains $5$ red balls, $4$ green balls and $7$ white balls. A ball is drawn at random from the box. Find the probability that the ball drawn is&#160;neither red nor white?

Question 22 : If $A$ and $B$ are independent events such that $P(A)&gt; 0$ and $P(B)&gt; 0$, then

Question 23 : Two persons $A$ and $B$ throw a coin alternatively till one of them gets head and wins the game. Find the respective probabilities of&#160; winning the&#160; game?

Question 24 : A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the arts becomes defective. What is the probability that the machine will not stop working?

Question 26 : A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

Question 27 : An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter driver, car driver and a truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is

Question 28 : Assertion: For two events A &amp; B such that $ P\left ( A \right )= P\left ( A/B \right )=\displaystyle \dfrac{1}{4} $ &amp; $ P\left ( B/A \right )=\displaystyle \dfrac{1}{2} $ then $ P\left ( \bar{A}/B \right )=\displaystyle \dfrac{3}{4} $ &amp; $ P\left ( \bar{B}/A \right )=\displaystyle \dfrac{1}{2} $. Reason: Two events A & B are independent then $ P\left ( B/A \right )= P\left ( B \right ) $.

Question 29 : If $P(A/B)=P(B/A)$. $A$ and $B$ are two non-mutually exclusive events then

Question 30 : Suppose four balls labelled $1, 2, 3, 4$ are randomly placed in boxes $B_{1}, B_{2}, B_{3}, B_{4}$. The probability that exactly one box is empty is

Question 31 : Two integers are selected at random from the set ${1,2,...,11}$. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:

Question 32 : A and B are two events such that $P(\overline A)=0.3, P(\overline B)=0.25$ and $P(\overline A\cap \overline B)=0.2$ then $P\left (\dfrac {A}{B}\right )$ is<br/>

Question 33 : Assertion: If $ P\left ( A/B \right )= P\left ( B/A \right ) $. A, B are two non mutually exclusive events then $ P\left ( A \right )= P\left ( B \right ) $. Reason: For non mutually exclusive events $ \left ( A\cap B \right )\neq \phi $ and $ P\left ( A/B \right )= \displaystyle \frac{P\left ( A\cap B \right )}{P\left ( B \right )} $, $P\left ( B/A \right )= \displaystyle \frac{P\left ( A\cap B \right )}{P\left ( A \right )} $.

Question 34 : A couple has $2$ children. The probability that both are boys, if it is known that at least one of the children is a boy is

Question 35 : In a series of 3 one-day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively. If a win, loss or draw gives 2, 0 and 1 point respectively, then what is the probability that team A will score 5 points in the series?

Question 36 : Two buses A and B are scheduled to arrive at a town central bus station at noon. The probability that bus A will be late is 1/5. The probability that bus B will be late is 7/25. The probability that the bus B is late given that bus A is late is 9/10. Then the probabilities<br>(i) neither bus will be late on a particular day and<br>(ii) bus A is late given that bus B is late, are respectively<br>

Question 37 : If $\overset { \_&#160; }{ E } $ and $\overset { \_&#160; }{ F } $ are the complementary events of events $E$ and $F$ respectively and if $0&lt;P(F)&lt;1$, then:<br/>

Question 38 : If $A$ &amp; $B$ are two events such that $P(A)=0.6$ &amp; $P(B)=0.8$, then the greatest value that $P(A/B)$ can have is

Question 39 : A garage mechanic keeps a box of good springs to use as replacements on customers cars.&#160;The box contains $5$ springs. A colleague, thinking that the springs are for scrap, tosses&#160;three faulty springs into the box. The mechanic picks two springs out of the box while&#160;servicing a car. Find the probability that&#160;the second spring drawn is faulty.<br/>

Question 40 : A salesman has a $70\%$ chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B?

Question 41 : Two dice of different colours are thrown at a time. The probability that the sum is either $7$ or $11$ is

Question 42 : Urn $A$ contains $6$ red and $4$ black balls and urn $B$ contains $4$ red and $6$ black balls. One ball is drawn at random from urn $A$ and placed in urn $B$. Then one ball is drawn at random from urn $B$ and placed in urn $A$. If one ball is now drawn at random from urn $A$, the probability that it is red is

Question 43 : There are $4$ balls of different colours &amp; $4$ boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that exactly no ball go to the box of its own colour is:

Question 44 : If $\displaystyle \bar{E}$ and$\displaystyle \bar{F}$ are the complementary events of the events $E$ and $F$ respectively then

Question 45 : A card is drawn from a deck of cards. What is the probability that it is either a spade or an ace or both&#160;

Question 46 : A quadratic equation $ax^2 + bx + c = 0$, with distinct coefficients is formed. It a, b, c are chosen from the numbers $2, 3, 5$ then the probability that the equation has real roots is

Question 47 : If $A, B, C$ are three events associated with a random experiment, then $P(A) P\left (\dfrac {B}{A}\right )P\left (\dfrac {C}{A} \cap B\right )$is

Question 48 : Two coins are tossed. Find the conditional probability that two Heads will occur giventhat at least one occurs.

Question 49 : There is $25$% chance that it rains on any particular day. What is the probability that there is at least one rainy day within a period of $7$ days?

Question 50 : A committee of three persons is to be randomly selected from a group of three men and two women and the chair person will be randomly selected from the committee.The probability that the committee will have exactly two women and one man, and that the chair person will be a women, is / are

Question 51 : If $E_1$ denotes the events of coming sum $6$ in throwing two dice and $E_2$ be the event of coming $2$ in any one of the two, then $P\left (\dfrac {E_2}{E_1}\right)$ is&#160;&#160;

Question 52 : Rajdhani Express stops at six intermediate stations between Kota and Mumbai.Five passengers board at Kota. Each passengers can get down at any station till Mumbai. The probability that all five passengers will get down at different stations, is

Question 53 : For two independent events $A$ and $B$, which of the following pair of events need not be independent?<br/>

Question 54 : A pair of numbers is picked up randomly (without replacement ) from the set $\{1,2,3,5,7,11,12,13,17,19\}$. The probability that the number $11$ was picked given that the sum of the number was even is nearly:

Question 55 : Two coins are tossed. What is the conditional probability that two heads result, given that there is at least one head ?

Question 56 : In a class, 40% of the students study math and science. 60% of the students study math. What is the probability of a student studying science given he/she is already studying math?<br>

Question 57 : Choose the most appropriate option.<br>$12$ defective pens are accidentally mixed with $132$ good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.<br>

Question 58 : If two events A and B such that $P(A')=0.3, P(B)=0.5$ and $P(A\cap B)=0.3$, then $P(B|A \cup B')$ is

Question 59 : A parents has two children. If one of them is boy, then the probability that other is, also a boy, is

Question 60 : If &#160;$P\left ( \dfrac{A}{C} \right )&gt; P\left ( \dfrac{B}{C} \right )$ &#160;and &#160;$P\left ( \dfrac{A}{\bar{C}} \right )&gt; P\left ( \dfrac{B}{\bar{C}} \right )$ &#160;then&#160;the&#160;relationship between $P(A)$ and $P(B)$ is

Question 61 : From a batch of $100$ items of which $20$ are defective, exactly two items are chosen, one at a time, without replacement. Calculate the probabilities that&#160;the second item chosen is defective.&#160;<br/>

Question 62 : A box contains $7$ tickets, numbered from $1$to $7$inclusive. If $3$tickets are drawn from the box without replacement, one at a time, determine the probability that they alternatively either odd-even-odd or even -odd - even.