Equally Likely Events

Q.

If $\text{A}$ and $\text{B}$ are two events such that $\text{P(A)}$ $\text{=}$ $\frac{1}{3}$, $\text{P(B)}$ $\text{=}$ $\frac{1}{4}$ and $\text{P(A∩B)}$ $\text{=}$ $\frac{1}{5}$, then $P\left(\frac{B}{A}\right)$ $\text{=}$?

1. $\frac{37}{40}$

2. $\frac{37}{45}$

3. $\frac{23}{40}$

4. None of these

Q.

A and B having equal skill, are playing a game of best of 5 points. After A has won two points and B has won one point, the probability that A will win the game is:

1. None

2. 3/4

3. 2/3

4. 1/2

Q. Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years.

1. 
2. 
3. 
4. 

Q. If $P(A\cap B)=\frac{7}{10}$ and $P\left(B\right)=\frac{17}{20},$ where $P$ stands for probability, then $P\left(A|B\right)$ is equal to

1. $\frac{7}{8}$
2. $\frac{17}{20}$
3. $\frac{14}{17}$
4. $\frac{1}{8}$

Q. Four men and three women are standing in a line for railway ticket. The probability of standing them in alternate manner is

1. $\frac{1}{35}$
2. $\frac{1}{33}$
3. $\frac{1}{84}$
4. $\frac{1}{7}$

Q. The probability that a non leap year selected at random will have $53$ Sundays is

1. $0$
2. $\frac{1}{7}$
3. $\frac{2}{7}$
4. $\frac{3}{7}$

Q.

The four faces of a regular tetrahedron are marked $A,B,C$ and $D$ and it is thrown twice.

1. Write all the possible outcomes namely $AA,AB,$ etc.
2. How many outcomes are there in all?
3. How many outcomes are there with both the letters are the same?

Q. Two real numbers $x,y$ are chosen from the interval $[0,8]$ then the probability that $y^2>2x$ is

1. $\frac{1}{6}$
2. $\frac{1}{3}$
3. $\frac{2}{3}$
4. $\frac{2}{9}$

Q.

Determine $P\left(\frac{E}{F}\right)$
A die is thrown three times
E: 4 appears on the third toss
F: 6 and 5 appears, respectively on first two tosses.

Q.

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

(A) 1 (B) 2 (C) 5 (D)

Q. The probability that $A$ speaks truth is $\frac{4}{5},$ while this probability for $B$ is $\frac{3}{5}.$ The probability of at least one of them is true when asked to speak on an event is

1. $\frac{3}{25}$
2. $\frac{2}{25}$
3. $\frac{4}{25}$
4. $\frac{23}{25}$

Q. A person goes to office by car or scooter or bus or train, probability of which are $\frac{1}{7},\frac{3}{7},\frac{2}{7}$ and $\frac{1}{7}$ respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is $\frac{2}{9},\frac{1}{9},\frac{4}{9}$ and $\frac{1}{9}$ respectively. Given that he reached office in time, the probability that he travelled by a car is

1. $\frac{1}{7}$
2. $\frac{2}{7}$
3. $\frac{3}{7}$
4. $\frac{4}{7}$

Q. If $p$ is selected from the set $\{1,2,3,......100\}$, then the probability of selecting $p$ such that the number $2^p+3^p+5^p$ is divisible by $4$ is

Q. For three events $A,B$ and $C,P$ (exactly one of the events $A$ occur) $=$ P (exactly one of the events B and C occur) $=$ P (exactly one of the events C or A occurs) $=$ p and P (all the three events occur simultaneously) $=p^2$, where $0<p<1/2$. If the probability of at least one of the three events $A,B$ and $C$ occurs is $11/18$, the value of $p$ is

1. $1/6$
2. $1/4$
3. $1/5$
4. $1/3$

Q. n cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is

1. $\frac{2}{n}$
2. $\frac{1}{n}$
3. $\frac{2}{(n-1)!}$
4. $Noneofthese$

Q.

An urn contains 5 red and 2 black balls. Two balls are randomly selected. Let X represent the number of black balls. What are the possible values of X? Is X a random variable?

Q. A number is randomly selected from the list:
1, 3, 3, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 10.
X = {3 is selected}
Y = {6 is selected}
X and Y are events.

1. equally likely
2. not equally likely
3. exhaustive

Q. You have your notebook with you. We know it has 6 faces. Top, bottom, one thin one at left, one at right and front and back faces.
Now you throw the notebook. We have sample space S = {1, 2, 3, 4, 5, 6} where these numbers represent each of the six faces of the book on which it may land (in final stable state) when you throw it.
All the outcomes in the sample space are equally likely.

1. True
2. False

Q. A number is randomly selected from the following list.
$1,3,3,6,6,6,8,8,8,8,10,10,10,10.$
Following events are described
X = {3 is selected}
Y = {6 is selected}
X and Y are equally likely events.

1. True
2. False

Q.

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

(A) 1 (B) 2 (C) 5 (D)

Q. In a class there are $10$ men and $20$ women. Out of them half of the number of men and half of the number of women have brown eyes. Out of them if a person is chosen at random, the chance that for the person chosen to be a man or brown eyed person is

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

Q.

A die is rolled and two events A and B are defined as follows.
A: An odd number turns up
B: A prime Number turns up

Find the value of 36 P$(A\cup B)$.

___

Q. A number is randomly selected from the following list.
$1,3,3,6,6,6,8,8,8,8,10,10,10,10.$
Following events are described
X = {3 is selected}
Y = {6 is selected}
X and Y are equally likely events.

1. True
2. False

Q. n cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is

1. $\frac{2}{n}$
2. $\frac{1}{n}$
3. $\frac{2}{(n-1)!}$
4. $Noneofthese$

Q. Transform the below sentence by replacing the word-"if" with the most appropriate word:
If I knew about this, I would not have allowed you to play with those kids.

1. Had I known about this, I would not have allowed you to play with those kids.
2. Whether I knew about this, I would not have allowed you to play with those kids.
3. Were I known about this, I would not have allowed you to play with those kids.
4. Have I known about this, I would not have allowed you to play with those kids.

Q. The probability that ${13}^{\text{th}}$ day of a randomly chosen month is a Friday is

1. $\frac{1}{7}$
2. $\frac{1}{84}$
3. $\frac{1}{12}$
4. $\frac{1}{42}$

Q. n cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is

1. $\frac{2}{n}$
2. $\frac{1}{n}$
3. $\frac{2}{(n-1)!}$
4. $Noneofthese$

Q. In a multiple choice question there are four alternative answers of which one or more than one is correct. A candidate will get marks on the question only if he ticks the correct answers. The candidate decides to tick answers at random. If he is allowed upto three chances to answer the question, find the probability that he will get marks on it.

Q. A number is randomly selected from the following list.
$1,3,3,6,6,6,8,8,8,8,10,10,10,10.$
Following events are described
X = {3 is selected}
Y = {6 is selected}
X and Y are equally likely events.

1. True
2. False

Q. You have your notebook with you. We know it has 6 faces. Top, bottom, one thin one at left, one at right and front and back faces.
Now you throw the notebook. We have sample space S = {1, 2, 3, 4, 5, 6} where these numbers represent each of the six faces of the book on which it may land (in final stable state) when you throw it.
All the outcomes in the sample space are equally likely.

1. False
2. True