1. ## Basic Probability Question

I have a question regarding basic proability. In the problem outlined below I am worried that I have calculated incorrectly. More specifically, I think I may have calculated the "compliment" of (M) instead of (M) itself. The answer I come up with is p(M) =.82. Given the problem and question below, am I wrong and how do I go about it correctly ? Thus far, all I have deduced from the problem is this:
p(A) = .18, p(A n M) = 0.11, and p(A u M)= 0.3.

Problem:
Assume you have applied for two scholarships, a Merit scholarship (M), and an Athletic scholarship (A). The probability that you receive and Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the following scholarships is 0.3.

Question:
What is the probability that you will receive a Merit scholarship ?

(there are more parts to this question but I am stuck on this part and without knowing the correct p(M), I will not be able to solve the rest of it)

2. Let's go back to the basic identity of two probablity:

p(a or b) = p(a) + p(b) - p(a and b)

replace b with m:

p(a or m) = p(a) + p(m) - p(a and m)

rearrange:

p(m) = p(a or m) - p(a) + p(a and m)

sub the probably:

p(m) = .3 - .18 + .11 = .23

3. ....Thanks....

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