A die thrown twice; sum observed is a multiple of 4.

Question

A die thrown twice; sum observed is a multiple of 4. Find the conditional probability that 4 appeared at least once.

Accepted Answer

$E_1$ (sum multiple of 4): $(1,3),(3,1),(2,2),(2,6),(6,2),(3,5),(5,3),(4,4),(6,6)$ --- 9 outcomes.

$E_1\cap E_2$ (4 appeared at least once): only $(4,4)$.

$$P(E_2\mid E_1) = \frac19$$

Solutions · 1