Algebra Examples

$p (a) = \frac{1}{6}$ , $p (b) = \frac{3}{7}$

Step 1

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

$P (a \cap b) = P (b \cap a) = P (a) \cdot (P (b))$

Step 2

Fill in the known values.

$P (a \cap b) = P (b \cap a) = \frac{1}{6} \cdot \frac{3}{7}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $6$ .

$P (a \cap b) = P (b \cap a) = \frac{1}{3 (2)} \cdot \frac{3}{7}$

Step 3.2

Cancel the common factor.

$P (a \cap b) = P (b \cap a) = \frac{1}{3 \cdot 2} \cdot \frac{3}{7}$

Step 3.3

Rewrite the expression.

$P (a \cap b) = P (b \cap a) = \frac{1}{2} \cdot \frac{1}{7}$

Step 4

Multiply $\frac{1}{2}$ by $\frac{1}{7}$ .

$P (a \cap b) = P (b \cap a) = \frac{1}{2 \cdot 7}$

Step 5

Multiply $2$ by $7$ .

$P (a \cap b) = P (b \cap a) = \frac{1}{14}$