Statistics Examples

$P (A) = 0.05$ , $P (B) = 0.5$ , $P (A a n d B) = 0.3$

Step 1

When $A$ and $B$ are not mutually exclusive events, the probability of $A$ or $B$ occurring is $P (A \cup B) = P (A) + P (B) - P (A \cap B)$ , which is called the addition rule for not mutually exclusive events $A$ and $B$ .

$P (A \cup B) = P (A) + P (B) - P (A \cap B)$

Step 2

Fill in the known values.

$P (A \cup B) = 0.05 + 0.5 - (0.3)$

Step 3

Multiply $- 1$ by $0.3$ .

$P (A \cup B) = 0.05 + 0.5 - 0.3$

Step 4

Add $0.05$ and $0.5$ .

$P (A \cup B) = 0.55 - 0.3$

Step 5

Subtract $0.3$ from $0.55$ .

$P (A \cup B) = 0.25$

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