# Probability

• Jul 30th 2008, 07:16 AM
hrunup
Probability
Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.
What is the probability that you will receive a Merit scholarship?

What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?

What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?

Need help
• Jul 30th 2008, 08:04 AM
Plato
$\displaystyle P(M \cup A)\quad {\mbox{means at least one}}$ and $\displaystyle P(M \cap A)\quad {\mbox{means both}}$.
You know that $\displaystyle P(M \cup A) = P(M) + P(A) - P(M \cap A)$.
Now solve for $\displaystyle P(M)$.
• Jul 30th 2008, 03:57 PM
mr fantastic
Quote:

Originally Posted by hrunup
Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.
What is the probability that you will receive a Merit scholarship?

What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?

What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?
$\displaystyle \Pr(A | M) = \frac{\Pr(A \cap M)}{\Pr(M)}$.
$\displaystyle \Pr(M | A) = \frac{\Pr(M \cap A)}{\Pr(A)} = \frac{\Pr(A \cap M)}{\Pr(A)}$.