Question

Suppose the probability that a company will be awarded a certain contract is .25, the probability that it will be awarded a second contract is .21 and the probability that it will get both contracts is .13. What is the probability that the company will win at least one of the two contracts?

Answer 1

33% probability that the company will win at least one of the two contracts

Explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a company is awarded the first contract.

B is the probability that a company is awarded the second contract.

We have that:

`A = a + (A \cap B)`

In which a is the probability that a company is awarded the first contract but not the second and
`A \cap B` is the probability that a company is awarded both contract.

By the same logic, we have that:

`B = b + (A \cap B)`

The probability that it will get both contracts is .13.

This means that
`A \cap B = 0.13`

The probability that it will be awarded a second contract is .21

This means that
`B = 0.21`

`B = b + (A \cap B)`

`0.21 = b + 0.13`

`b = 0.08`

The probability that a company will be awarded a certain contract is .25

This means that
`A = 0.25`

`A = a + (A \cap B)`

`0.25 = a + 0.13`

`a = 0.12`

What is the probability that the company will win at least one of the two contracts?

`A \cup B = a + b + A \cap B = 0.12 + 0.08 + 0.13 = 0.33`

33% probability that the company will win at least one of the two contracts