PnC

Q.

A committee of two persons is selected from two men and two women. What is the probability that the committee will have

(i) no man?

(ii) one man?

(iii) two men?

Q.

A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has

(i) all boys?

(ii) all girls?

(iii) 1 boy and 2 girls?

(iv) at least one girls?

(v) at most one girls?

Q.

Five different marbles are placed in 5 different boxes randomly. Then the probability that exactly two boxes remain empty is (each box can hold any number of marbles).

1. $\frac{2}{5}$
2. $\frac{12}{25}$
3. $\frac{3}{5}$
4. None of these

Q.

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that :

(i) all are blue?

(ii) at least one is green?

Q.

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

1. $\frac{5}{84}$

2. $\frac{3}{9}$

3. $\frac{3}{7}$

4. $\frac{7}{17}$

Q.

A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that

(i) all the three balls are blue balls

(ii) all the balls are of different colours.

Q.

Six boys and six girls sit in a row randomly.

The probability that all girls sit together is

1. $\frac{1}{102}$

2. $\frac{1}{122}$

3. $\frac{1}{112}$

4. $\frac{1}{132}$

Q. Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is

1. $\frac{3}{9}$
2. $\frac{8}{9}$
3. $\frac{5}{9}$
4. $\frac{4}{9}$

Q.

Three numbers are chosen from 1 to 20. The probability that they are not consecutive is

1. $\frac{186}{190}$

2. $\frac{187}{190}$

3. $\frac{18}{{}^{20}{C}_3}$

4. $\frac{188}{190}$

Q.

A committee of five is to be chosen from a group of $9$people. The probability that a certain married couple will either serve together or not at all is

1. $\frac{1}{2}$

2. $\frac{5}{9}$

3. $\frac{4}{9}$

4. $\frac{2}{3}$

Q.

6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is

1. None of these

2. $\frac{1}{432}$

3. $\frac{12}{431}$

4. $\frac{1}{132}$

Q. A box contain 10 mangoes out of which four are rotten. Two mangoes are taken out together. If one of them is found good and p is probability the other is also good, then value of 13p is ___.

Q.

If the letters of the word 'MISSISSIPPI' are written down at random in a row, what is the probability that four S's come together.

Q.

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Q.

Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is

1. $\frac{{}^5{P}_5}{5^5}$

2. $\frac{{}^7{P}_5}{7^5}$

3. $\frac{7^5}{7_5^P}$

4. $\frac{6}{6_5^P}$

Q. Words with or without meaning are to be formed using all the letters of the word $\text{EXAMINATION}$. The probability that the letter $\text{M}$ appears at the fourth position in any such word is

1. $\frac{1}{66}$
2. $\frac{1}{11}$
3. $\frac{1}{9}$
4. $\frac{2}{11}$

Q.

Two cards are drawn from a well shuffled pack of 52 cards. Find the

probability that either both are black or both are kings.

Q.

Five cards are drawn from a pack of 52 cards.
What is the chance that these 5 will contain :
(i) just one ace

(ii) at least one ace?

Q.

Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively?

1. $\frac{1}{462}$

2. $\frac{1}{924}$

3. $\frac{1}{2}$

4. None of these

Q.

Three numbers are chosen at random from numbers 1 to 30. Write the probability that the chosen numbers are consecutive.

Q.

There are four hotels in a town. If $3$ men check into the hotels in a day, then what is the probability that each checks into a different hotel?

1. $\frac{6}{7}$

2. $\frac{1}{8}$

3. $\frac{3}{8}$

4. $\frac{5}{9}$

Q.

Out of $13$ applicants for a job, there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that at least one of the selected persons will be a woman is:

1. $\frac{25}{39}$

2. $\frac{14}{39}$

3. $\frac{5}{13}$

4. $\frac{10}{13}$

Q.

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that

(i) both the balls are red

(ii) one ball is red and the other is black

(iii) one ball is white.

Q.

Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.

Q. What is the mean of $f\left(x\right)=3x+2$ where $x$ is a random variable with probability distribution
$\begin{array}{ccccc}X=x& 1& 2& 3& 4\\ P(X=x)& \frac{1}{6}& \frac{1}{3}& \frac{1}{3}& \frac{1}{6}\end{array}$

1. $\frac{19}{2}$
2. $\frac{15}{2}$
3. $\frac{5}{3}$
4. $\frac{5}{2}$

Q.

From a well shuffled deck of 52 cards, 4 cards are drawn at random. What

is the probability that all the drawn cards are of the same colour.

Q. $A$ and $B$ are two independent witnesses (i.e., there is no collusion between them) in a case. The probability that $A$ will speak the truth is $x$, and the probability that $B$ will speak the truth is $y$. $A$ and $B$ agree in a certain statement. Then the probability that this statement is true is:

1. $\frac{xy}{1-x-y+2xy}$
2. $\frac{xy}{1-x-y+xy}$
3. $\frac{xy}{1-2x-y+xy}$
4. $\frac{xy}{1+x+2y-xy}$

Q.

A bag contains tickets numbered from I to 20. Two tickets are drawn. Find the probability that

(i) both the tickets have prime numbers on them

(ii) on one there is a prime number and on the other there is a multiple of 4.

Q. The probability of hitting a target by three men is $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that atleast two of them hit the target is $\mu$ then $\lambda +\mu$ is -

1. $\frac{13}{24}$
2. $\frac{6}{24}$
3. $\frac{7}{24}$
4. $\frac{12}{24}$

Q. If the letters in the word $CALCULUS$ are arranged in all possible manners (any arrangement is considered a word, for example $CCLLAUUS$ would be considered a word), then the probability that the $2U^{\prime }s$ are together, is

1. $\frac{1}{6}$
2. $\frac{1}{5}$
3. $\frac{1}{4}$
4. $\frac{1}{3}$