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GRE Quantitative Reasoning QUESTION #8157
Question 1

Let $p$ be the probability that event $E$ will occur, and let $s$ be the probability that event $E$ will not occur. Compare:

Quantity A: $p + s$

Quantity B: $ps$

  • Quantity A is greater✔️
  • Quantity B is greater
  • The two quantities are equal
  • The relationship cannot be determined from the information given
Correct Answer Explanation

Since $p$ and $s$ are complementary probabilities: $p + s = 1$ (one of them must happen).

So Quantity A $= 1$.

For Quantity B: $ps = p(1-p)$. Since $0 \leq p \leq 1$, the product $p(1-p) \leq \dfrac{1}{4}$ (maximum at $p = 0.5$).

Therefore $ps \leq 0.25 < 1 = p + s$.

Quantity A is always greater.