Mathematics : Probability

In a simultaneous toss of 4 coins, what is the probability of getting exactly

(a) 4 heads?                           (b) 3 heads?

In a class of 25 students with roll numbers 1 to 25, one student is picked at random. Find the probability that the roll number picked is a multiple of:

(a) 5 or 7                      
(b) 2 or 3
(c) neither a multiple of 5 nor of 7
(d) neither a multiple of 2 nor of 3.

Two dice are tossed. What is the probability that the sum of numbers appearing on them is:

(a) divisible by 2 and by 3?

(b) divisible by 2 or by 3?

(c) divisible by 5 or by 9?

For two events A and B, P(not A) =  P(A) = p, P(B) = q,  Find values of p and q.

A card is drawn from a well shuffled pack of 52 cards. Events A and B are:

A : the card is a diamond card.

B : the card is a queen.

Determine whether P (A ∩ B) = P(A) x P(B)

A die is rolled thrice. What the probability of:

(a) not getting a six each time?

(b) getting the same number each time?