Question

1. You have applied for two scholarships: the TRIO Opportunity Grant (TOG) and the Vermont Opportunity in Education (VEOP) scholarship. From data collected over the years, the probability that you receive the VEOP scholarship is 0.25, the probability that you receive both scholarships is 0.15, and the probability that you get at least one of these scholarships is 0.37. a. What is the probability that you receive the TOG

Answer 1

0.27 = 27% probability that you receive the TOG scolarship.

Explanation:

I am going to solve this question treating these probabilities as Venn probabilities.

I am going to say that:

Event A: TOG scolarship

Event B: VEOP scolarship

The probability that you receive the VEOP scholarship is 0.25

This means that
`P(B) = 0.25`

Probability that you receive both scholarships is 0.15

This means that
`P(A \cap B) = 0.15`

The probability that you get at least one of these scholarships is 0.37.

This means that
`P(A \cup B) = 0.37`

What is the probability that you receive the TOG?

This is P(A). These measures are related by:

`P(A \cup B) = P(A) + P(B) - P(A \cap B)`

So

`P(A) = P(A \cup B) + P(A \cap B) - P(B)`

Replacing with the values in this question

`P(A) = 0.15 + 0.37 - 0.25 = 0.27`

0.27 = 27% probability that you receive the TOG scolarship.