Three groups A, B and C are contesting for positions on the Board of Directors of a company. The probability of their winning are 0.5, 0.3 and 0.2, respectively. If the froup A wins, then the probabilityof introducing a new product is 0.7 and the corresponding probabilies for groups B and C are 0.6 and 0.5, respectively. Find the probability that the new product will be introduced.

Two groups are competing for the positions of the board of Directors of a Corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further if the first group wins the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.

Three persons A,B and C fire a target in turn . Their probabilities of hitting the target are 0.4 , 0.3 and 0.2 respectively . The probability of two hits is

Three persons A,B and C, fire at a target in turn, starting with A. Their probability of hitting the target are 0.4, 0.3 and 0.2, respectively. The probability of two hits is

In a horse -race, the probabilities to win the race for three horses A,B and C are 1/4,1/5 and 1/6 respectively. Find the probability to win the race of any one horse.

If the probability for A to fail in an examination is 0.2 and that for B is 0,3 , then the probability that either A or B fails is

The probability of two events A and B are 0.25 and 0.50 respectively. The probability of their simultaneous occurrences 0.15. Find the probability that neither A nor B occurs.

If the probabilities for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is

The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is…..

The probability that a student will receive A, B, C or D grade or 0.40, 0.3, 0.1 and 0.10 respectively. Find the probability that a student will receive. i. B or C grade ii. at most C grade.

The probability of an event A occurring is 0.5 and of B is 0.3. If A and B are mutually exclusive events then the probability of neither A nor B occurring is