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 $5$ .

$P (c \cap d) = P (d \cap c) = \frac{6}{25}$