Solutions - 5030-07

(1) Define events:

Let $W_{1}$ be the event where the Winning Fund outperforms the first year.

Let $W_{2}$ be the event where the Winning Fund outperforms the second year.

We are asked to compute $P [W_{1} \cap W_{2}]$ .

(2) Identify given probabilities:

$P [W_{1}] = 0.15$

$P [W_{2} | W_{1}] = 0.3$

(3) Apply the multiplication rule:

\begin{matrix} P [W_{1} \cap W_{2}] = P [W_{1}] \cdot P [W_{2} | W_{1}] \\ ≫ ≫ 0.15 \cdot 0.3 ≫ ≫ 0.045 \end{matrix}

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