If X follows a binomial distribution with parameters n = 100 and p = $\frac{1}{3}$ then P(X = r) 3 is maximum when r is equal to

• 16

• 32

• 33

• none of these

A random variable X takes values 0, 1, 2, 3, ... with probability P(X = x) = k(x + 1)${\left(\frac{1}{5}\right)}^{\mathrm{x}}$, where k is constant, then P(X = 0) is

• 7/25

• 18/25

• 13/25

• 16/25

Out of 15 persons 10 can speak Hindi and 8 can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

• 3/5

• 7/12

• 1/5

• 2/5

74.

A random variable X has the following probability distribution

X = x1	1	2	3	4
P(X = x1)	0.1	.02	0.3	0.4

The mean and the standard deviation are respectively

• 3 and 2

• 3 and 1

• $3 \mathrm{and} \sqrt{3}$

• 2 and 1

The probability distribution of a random variable X is given as

Then, the value of p is

• $\frac{1}{72}$

• $\frac{3}{73}$

• $\frac{5}{72}$

• $\frac{1}{74}$

If n(A) = 43, n(B) = 51 and n(A ∪ B) = 75, then n[(A - B) $\cup$ (B - A)] is equal to

• 53

• 45

• 56

• 66

If five dices are tossed, then what is the probability that the five numbers shown will be different?

• $\frac{5}{54}$

• $\frac{5}{18}$

• $\frac{5}{27}$

• $\frac{5}{81}$

If the events A and B are independent and if $\mathrm{P}\left(\overline{\mathrm{A}}\right) = \frac{2}{3}, \mathrm{P}\left(\overline{\mathrm{B}}\right) = \frac{2}{7}$, then $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$ is equal to

• $\frac{4}{21}$

• $\frac{3}{21}$

• $\frac{5}{21}$

• $\frac{2}{21}$

Two fair dice are rolled. Then, the probability of getting a composite number as the sum of face values is equal to

• $\frac{7}{12}$

• $\frac{5}{12}$

• $\frac{1}{12}$

• $\frac{3}{4}$

Let S be the set of all 2 x 2 symmetric matrices whose entries are either zero or one. A matrix X is chosen from S. The probability that the determinant of X is not zero is

• 1/3

• 1/2

• 3/4

• 1/4