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:

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

If A and B are two events such that $A \neq \emptyset$, B $\neq \emptyset$, then which of following is/are TRUE:

A. $P(B/A)=P(A).P(B)$

B. $P(B/A)=\frac{P(A\cap B)}{P(A)}$

C. $P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}$

D. $P(B/A).P(A/B)=2$

Choose the correct answer from the options given below:

A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black resulted in a 5 is

If in a binomial distribution $n = 4$, $P(X=0) = \frac{16}{81}$, then $P(X=4)$ equals :

A bag contains 4 red and 6 black balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is black is

A fair coin is tossed until a head or five tails occur. The probability distribution of the number of tosses is,