Final answer:
The probability that the aerospace company wins both defense contracts is found by multiplying the probability of winning the first contract with the probability of winning the second contract given the first is won, which is 0.36 × 0.73, resulting in a 26.28% chance of winning both.
Step-by-step explanation:
The question asks us to calculate the probability that an aerospace company wins both federal government defense contracts, given certain probabilities for winning each one independently based on the outcome of the first. To find the joint probability of winning both contracts, we can use the conditional probability formula.
The probability of winning the first contract is given as 36% (or 0.36). If they win the first contract, the probability of winning the second is given as 73% (or 0.73).
Therefore, the joint probability of winning both contracts after winning the first one can be calculated as
P(Win first AND Win second) = P(Win first) × P(Win second | Win first)
= 0.36 × 0.73.
Thus, the probability that they win both contracts is 0.2628 or 26.28%.