If $\mathrm{P}\left(\mathrm{A}\right) = \frac{1}{2}, \mathrm{P}\left(\mathrm{B}\right) = \frac{1}{3} \mathrm{and} \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \frac{1}{4}$, then the value of $\mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right)$ wll be

• 1

• 0

• $\frac{1}{2}$

• $\frac{1}{3}$

Six boys and six girls sit in a row. The probability that the boys and girls sit alternately will be

• $\frac{1}{462}$

• $\frac{1}{924}$

• $\frac{1}{2}$

• None of these

In a regular hexagon, 3 vertices out of 6 are randomly chosen. The probability that the triangle formed out of these three vertices will be an equilateral triangle, is

• $\frac{1}{2}$

• $\frac{1}{5}$

• $\frac{1}{10}$

• $\frac{1}{20}$

64.

In a competition A, B, C are participating the probability that A wins is twice that of B, the probability that B wins is twice that of C, then probability that A loses is

• $\frac{1}{7}$

• $\frac{2}{7}$

• $\frac{4}{7}$

• $\frac{3}{7}$

The probability that a number selected at random from the set of numbers (1, 2, 3, ... , 100) is a cube, is

• $\frac{1}{25}$

• $\frac{2}{25}$

• $\frac{3}{25}$

• $\frac{4}{25}$

A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected at random, the probability that it is a black or a red ball, is

• $\frac{1}{3}$

• $\frac{1}{4}$

• $\frac{5}{12}$

• $\frac{2}{3}$

The probability of getting qualified in IITJEE and EAMCET by a student are respectively $\frac{1}{5} \mathrm{and} \frac{3}{5}$. The probability that the student gets qualified for atleast one of these test, is

• $\frac{3}{25}$

• $\frac{8}{25}$

• $\frac{17}{25}$

• $\frac{22}{25}$

One die and a coin (both unbiased) are tossed simultaneously. The probability of getting 5 on the top of the die and tail on the coin is

• $\frac{1}{2}$

• $\frac{1}{12}$

• $\frac{1}{6}$

• $\frac{1}{8}$

A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ballis drawn from it. Then, the probability for the ball chosen be white, is :

• $\frac{2}{15}$

• $\frac{7}{15}$

• $\frac{8}{15}$

• $\frac{14}{15}$

A random variate X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X = 3) = 2P(X = 1) and P(X = 2) = 0.3, then P(X = 0) is equal to :

• 0.1

• 0.2

• 0.3

• 0.4