Algebra Examples

$p (A) = \frac{1}{4}$ , $P (B) = \frac{2}{7}$

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.

$P (A \cap B) = P (B \cap A) = \frac{1}{4} \cdot \frac{2}{7}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $4$ .

$P (A \cap B) = P (B \cap A) = \frac{1}{2 (2)} \cdot \frac{2}{7}$

Step 3.2

Cancel the common factor.

$P (A \cap B) = P (B \cap A) = \frac{1}{2 \cdot 2} \cdot \frac{2}{7}$

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 $7$ .

$P (A \cap B) = P (B \cap A) = \frac{1}{14}$