Algebra Examples

p (A) = \frac{1}{4}

$p (A) = \frac{1}{4}$ ,

P (B) = \frac{2}{7}

$P (B) = \frac{2}{7}$

Step 1

When

A

$A$ and

B

$B$ are independent events, the probability of

A

$A$ and

B

$B$ occurring is

P (A \cap B) = P (B \cap A) = P (A) \cdot (P (B))

$P (A \cap B) = P (B \cap A) = P (A) \cdot (P (B))$ , which is called the multiplication rule for independent events

A

$A$ and

B

$B$ .

P (A \cap B) = P (B \cap A) = P (A) \cdot (P (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}

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

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

4

$4$ .

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

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

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

$7$ .

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