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 73%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 46%. A. What is the probability that they win both contracts

The probability that they win both contracts is 33% if there is a 45% probability of winning the first contract and the probability of winning the second contract after winning the first contract.

What is probability?

Probability is the rate of successful outcomes to the total outcomes of an event.

P(E) = n(E)/n(S)

Where E -event, n(E) - successful/favorable outcomes of event E, and n(S) - total outcomes of the event.

Calculation:

It is given that,

An aerospace company has submitted bids on two separate federal government defense contracts.

The probability of winning the first contract is - 45%

The probability of winning the second contract if they win the first contract is - 73%

The probability of winning the second contract if they lose the first contact is - 45%

So, the probability that they win both contracts is

= (probability of winning the first contract) × (probability of winning the second contract)

= 0.45 × 0.73

= 0.3285 ≅ 0.33

⇒ 33%

Therefore, the probability that they win both contracts is 33%.

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