In: Statistics and Probability
An aeroplane company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 44% probability of winning the first contract. If they win the first contract , the probability of winning the second is 65%. However, if they lose the first contract the president thinks that the probability of winning the second contract decreases to 53%.
a.What is the probability that they win both contracts?
b.What is the probability that they lose both contracts?
c.What is the probability that they win only one contract?
P(winning first) = 0.44
P(winning second | win first) = 0.65
P(winning second | lose first) = 0.53
a) P(winning both the contracts) = P(winning second | win first) * P(win first) = 0.65 * 0.44 = 0.286
b) P(winning second) = P(winning second | win first) * P(win first) + P(winning second | lose first) * P(lose first)
= 0.65 * 0.44 + 0.53 * (1 - 0.44)
= 0.5828
P(winning. at least one contract) = P(winning first) + P(winning second) - P(winning both)
= 0.44 + 0.5828 - 0.286
= 0.7368
P(loosing both the contracts) = 1 - P(winning. at least one contract) = 1 - 0.7368 = 0.2632
c) P(win only one contract) = P(win only first) + P(win only second)
= P(win first) - P(win both) + P(win second) - P(win both)
= 0.44 - 0.286 + 0.5828 - 0.286
= 0.4508