A GRE - Probability Question?

Question

In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that H will occur is s, where both r and s are greater than 0. Quantity A The probability that either G will occur or H will occur, but not both. Quantity B r+s-rs A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given. The answer is B. How?

Answer 1

Quantity A: The probability that either G will occur or H will occur, but not both.

Quantity B: r+s-rs

Quantity A = P(G ∪ H) - P(G ∩ H) = P(G) + P(H) - 2P(G ∩ H) = P(G) + P(H) - 2P(G)P(H) = r + s - 2rs

Quantity B = r + s - rs

Quantity A = Quantity B - rs

Quantity A < Quantity B