An aerospace company has submitted bids on two separate fede

An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 45% probability of winning the first contract. If they win the first contract, the probability of winning the second is 85% However, if they lost the first contract, the president thinks that the probability of winning the second contract decreases to 35%

What is the probability that they win at least one contract?

PLEASE SHOW ME HOW YOU GET THE ANSWER

Solution

Note that

P(win at least one) = P(win 1st)P(win 2nd) + P(win 1st)P(lose 2nd) + P(lose 1st)P(win 2nd)

Thus,

P(win at least one) = 0.45*0.85 + 0.45*0.15 + 0.55*0.35

= 0.6425 [ANSWER]