Algebra Examples

$P (C) = \frac{2}{5}$ , $P (D) = \frac{3}{5}$

Step 1

When $C$ and $D$ are independent events, the probability of $C$ and $D$ occurring is $P (C \cap D) = P (D \cap C) = P (C) \cdot (P (D))$ , which is called the multiplication rule for independent events $C$ and $D$ .

$P (C \cap D) = P (D \cap C) = P (C) \cdot (P (D))$

Step 2

Fill in the known values.

$P (C \cap D) = P (D \cap C) = \frac{2}{5} \cdot \frac{3}{5}$

Step 3

Multiply $\frac{2}{5} \cdot \frac{3}{5}$ .

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Step 3.1

Multiply $\frac{2}{5}$ by $\frac{3}{5}$ .

$P (C \cap D) = P (D \cap C) = \frac{2 \cdot 3}{5 \cdot 5}$

Step 3.2

Multiply $2$ by $3$ .

$P (C \cap D) = P (D \cap C) = \frac{6}{5 \cdot 5}$

Step 3.3

Multiply $5$ by $5$ .

$P (C \cap D) = P (D \cap C) = \frac{6}{25}$