Question

An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 35% probability of winning the first contract. If they win the first contract, the probability of winning the second is 73%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 48%.1. What is the probability that they will lose both contracts? 2. What is the probability that they win only one contract? 3. What is the probability that they win both contracts?

Answer 1

1) 0.338

2) 0.4065

3) 0.2555

Explanation:

1. The probability that they will lose both contracts is the probability of losing contract 1 and 2 altogether:

The probability of losing contract 1 is: 1 - 0.35 = 0.65

The probability of losing contract 2, given that they lose contract 1 is: 1 - 0.48 = 0.52

The probability of losing both contracts is 0.65*0.52 = 0.338

2. The probability that they win only one contract is the probability they they win contract 1, lose contract 2, plus the probability that they lose contract 2, win contract 1:

0.35*(1-0.73) + (1-0.35)*0.48 = 0.0945 + 0.312 = 0.4065

3. The probability that they win both contract is

0.35 * 0.73 = 0.2555