Three dice having digits 1, 2, 3, 4, 5 and 6 on their faces are marked I, II and III and rolled. Let x, y and z represent the number on die-I, die-II and die-III respectively. What is the number of possible outcomes such that x > y > z ?

• 14

• 16

• 18

• 20

Which one of the following can be obtained from an ogive ?

• Mean

• Median

• Geometric mean

• Mode

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

• $\frac{1}{6}$

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{2}{3}$

A question is given to three students A, B and C whose chances of solving it are $\frac{1}{2}, \frac{1}{3} \mathrm{and} \frac{1}{4}$ respectively. What is the probability that the question will be solved ?

• $\frac{1}{24}$

• $\frac{1}{4}$

• $\frac{1}{2}$

• $\frac{23}{24}$

45.

The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. What is the number of boys in the class ?

• 50

• 55

• 60

• 100

For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If AB, then the values of conditional probabilities $\mathrm{P}\left(\overline{)\mathrm{A}}\mathrm{B}\right) \mathrm{and} \mathrm{P}\overline{)(\mathrm{B}}\mathrm{A})$ are respectively

• $\frac{2}{5}, \frac{3}{5}$

• $\frac{2}{5}, 1$

• 1, $\frac{2}{5}$

• Information is insufficient

A point is chosen at random inside a circle. What is the probability that the point is closer to the centre of the circle than to its boundary ?

• $\frac{1}{5}$

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{2}$

A card is drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that it is an ace ?

• $\frac{1}{13}$

• $\frac{2}{13}$

• $\frac{3}{13}$

• $\frac{1}{52}$

Consider the following statements:

1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other.
2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities. Which of the above statements is/are correct ?

• 1 only

• 2 only

• both 1 and 2

• neither 1 nor 2

If two fair dice are thrown, then what is the probability that the sum is neither 8 nor 9 ?

• $\frac{1}{6}$

• $\frac{1}{4}$

• $\frac{3}{4}$

• $\frac{5}{6}$