If two numbers are selected at random from the first 25 natural numbers, then the probability that their sum will be odd is:

The probability of simultaneous occurrence of at least one of two events E and F is $p$. If the probability that exactly one of E, F occurs is $q$, then $P(\overline{E}) + P(\overline{F})$ is equal to

Two numbers are selected at random from the integers 1 through 19. If the sum is even, then the probability that both are odd numbers is:

If A and B are two distinct events such that P(A|B) = P(B|A), then which of the following is /are possible?

(A) A= B

(B) P (A) = P(B)

(C) A ⊂ B but A ≠ B

(D) A∩ B = ɸ

Choose the correct answer from the options given below:

If a random variable y follows Poisson's distribution such that $P(X = 2) = 9 P(X = 4) + 90 P(X = 6)$, then sum of the mean and variance of X is

An alphabet has been selected from English alphabets. What is the probability that it is a vowel given that it precedes 'M' ?

In class XII, suppose 5% of boys and 0.25% of girls are physically fit for a game. A fit student is selected at random from this class having same number of boys and girls. If the probability that the selected student is a girl is $\frac{m}{n}$, gcd(m, n) = 1, then m + n is equal to