Two groups are competing for the position on 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

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.

Two sets of candidates are competing for the position on the board of directors of a company. The probabilities that the first and second sets will win are 0.6 and 0.4 respectively. If the first set wins, the probability of introducing a new product is 0.8 and the corresponding probability if the second set wins is 0.3. What is the probability that the new product will be introduced ?

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.

A machine operates only when all of its three components function The probabilities of the failures of the first , second and third component are 0.2, 0,3 and 0.5 respectively . What is the probability that the machine will fail ?

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.

10 boys and 2 girls are divided into 3 groups of 4 each.The probability that the girls will be in different groups is

A soldier is firing at a moving target. He fires four shots. The probability of hitting the target at the first, second, third and fourth shots are 0.6, 0.4, 0.2 and 0.1 respectively. What is the probability that he hits the target?