Three unbiased coins are tossed once. Find the probability of getting

at least 2 tails

Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is twice as likely to be selected as B, and B and C are given about the same chance of being selected, while C is twice as likely to be selected as D, what are the probabilities that

(a) C will be selected?

(b) A will not be selected?

If A and B are mutually exclusive events, then

State whether the statements are True or False

The probability of an occurrence of event A is .7 and that of the occurrence of event B is .3 and the probability of occurrence of both is .4.

If P (A ∪ B) = P (A ∩ B) for any two events A and B, then

State whether the statements are True or False

The probability of intersection of two events A and B is always less than or equal to those favourable to the event A.

If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45, find

(a) P (A′)

(b) P (B′)

(c) P (A ∪ B)

(d) P (A ∩ B)

(e) P (A ∩ B′)

(f) P (A′∩ B′)

The probability that a patient visiting a denist will have a tooth extracted is 0.06, the probability that he will have a cavity filled is 0.2, and the probability that he will have a tooth extracted or a cavity filled is 0.23.What is the probability that he will have a tooth extracted as well as a cavity filled?

A die is thrown twice. Each time the number appearing on it is recorded. Describe the following events:

(i) A = Both numbers are odd.

(ii) B = Both numbers are even

(iii) C = sum of the numbers is less than 6.

Also, find A ∪ B, A ∩ B, A ∪ C, A ∩ C. Which pairs of events are mutually exclusive.