Question

The Gable Construction Corporation has placed bids for installing electronic message boards on two different highways.

Because of competition from other companies, Gable Construction Corporation officials estimate that the probability that
they will be awarded the Macon Expressway contract is 0.65 and the probability that they will be awarded the Seaview
Expressway contract is 0.43. Furthermore, the probability that they will be awarded both contracts is 0.22. What is the
probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway

Answer 1

0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway

Explanation:

We solve this question using these events as Venn sets.

I am going to say that:

Event A: Awarded the Macon Expressway.

Event B: Awarded the Seaview Expressway.

Probability that they will be awarded the Macon Expressway contract is 0.65

This means that
`P(A) = 0.65`

The probability that they will be awarded the Seaview Expressway contract is 0.43.

This means that
`P(B) = 0.43`

Furthermore, the probability that they will be awarded both contracts is 0.22.

This means that
`P(A \cap B) = 0.22`

What is the

Probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway?

Only A:

`P(A) - P(A \cap B) = 0.65 - 0.22 = 0.43`

Only B:

`P(B) - P(A \cap B) = 0.43 - 0.22 = 0.21`

Either

0.43 + 0.21 = 0.64

0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway