Probability of independent events?

Question

The probability that George will get an A on his test is .2. The probability that Mary will get an A on her test is .2. Assuming independence, what is the probability that both will get an A? What is the probability that exactly 1 will get an A? What is the probability that at least one will get an A?

Here's what I think I need to do, but please confirm or correct.

P (George and Mary): (.2)(.2) = .04
P (George or Mary): (.2)+(.2) = .40
P (at least one): simply .2

Thanks!!

Answer 1

P(George) = 0.2
P(Mary) = 0.2

P(Both) = (0.2)(0.2) = 0.04

P(Neither) = (1 - 0.2)(1 - 0.2) = (0.8)(0.8) = 0.64

P(At least one) = 1 - P(Neither) = 1 - 0.64 = 0.36

P(Exactly one) = 1 - P(Neither) - P(Both)
P(Exactly one) = 1 - 0.64 - 0.04 = 0.32

Answer 2

In the first part: You need one of them to get an A but not the other. You started out right in finding P (George and Mary): (.2)(.2) = .04, but you also need to find the probability of neither getting an A (.8*.8) = .64. So one, but not both getting an A would be 1-.04+.64. The answer is 0.32.

To find at least one getting an a you just need to know the prob of neither getting an A. So 1-.64 = .36