A fair six-sided die is rolled. Let $E$ be “an even number” and $P$ be “a prime number”. A

Question

A fair six-sided die is rolled. Let $E$ be “an even number” and $P$ be “a prime number”. A student calculates: $$ P(E\cup P)=\frac36+\frac36=1. $$ List $E$, $P$, and their common outcomes. Explain the error. Find the correct probability of $E\cup P$. Find the probability of neither event.

Accepted Answer

(a) $E=\{2,4,6\}$, $P=\{2,3,5\}$, overlap $\{2\}$; (b) double-counted $2$; (c) $\frac{5}{6}$; (d) $\frac{1}{6}$.

Probability

Probability

Solution:

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