Statistics Examples

P (A) = 0.08

$P (A) = 0.08$ ,

P (B) = 0.2

$P (B) = 0.2$ ,

P (A a n d B) = 0.06

$P (A a n d B) = 0.06$

Step 1

When

A

$A$ and

B

$B$ are not mutually exclusive events, the probability of

A

$A$ or

B

$B$ occurring is

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

$P (A \cup B) = P (A) + P (B) - P (A \cap B)$ , which is called the addition rule for not mutually exclusive events

A

$A$ and

B

$B$ .

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

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

Step 2

Fill in the known values.

P (A \cup B) = 0.08 + 0.2 - (0.06)

$P (A \cup B) = 0.08 + 0.2 - (0.06)$

Step 3

Multiply

- 1

$- 1$ by

0.06

$0.06$ .

P (A \cup B) = 0.08 + 0.2 - 0.06

$P (A \cup B) = 0.08 + 0.2 - 0.06$

Step 4

Add

0.08

$0.08$ and

0.2

$0.2$ .

P (A \cup B) = 0.28 - 0.06

$P (A \cup B) = 0.28 - 0.06$

Step 5

Subtract

0.06

$0.06$ from

0.28

$0.28$ .

P (A \cup B) = 0.22

$P (A \cup B) = 0.22$

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