Probability?

Question

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?

Please help

Answer 1

C'mon, that's sneaky, trying to slip a probability question into the financial aid section, just because the word problem involves scholarships. The people who hang out in this area of the site are financial aid specialists!

Nonetheless...today is your lucky day.

The probability of two independent events both happening is defined as the product of the probability of each event happening independently.

Here, the probability of A is known - that's .18

We don't know the probability of M, that's what we need to figure out.

We do, however, know the probability of BOTH A and M happening, that's .11 (it said this in the problem)

So, using the multiplication rule I mentioned above:

Probability of A AND M = Prob (A) x Prob (M)

.11 = .18 x Prob(M)  

.11/.18 = Prob(M)

.61 = Prob(M)

So, the independent probability of the merit scholarship is .61

Now - for the second question - what is the probability of receiving the athletic scholarship given that you have been awarded the merit scholarship - that's a trick question, testing that you understand what it means for two events to be "independent". The probability of receiving the merit scholarship given that you have been awarded the athletic (and vice versa) are exactly the same as the probability of receiving each independently.

.18 for the athletic

.61 for the merit

As for the business about the probability of getting at least one of the 2 scholarships - they mentioned it, but they didn't ask you to do anything with that.

The formula is:

P(M) + P(A) - P(M)P(A)

(.61 + .18) - (.61)(.18) =

.43 - (.1098) = .3202

I hope that helped.