Statistics Examples

P (A) = 0.4

$P (A) = 0.4$ ,

P (B) = 0.01

$P (B) = 0.01$ ,

P (A a n d B) = 0.12

$P (A a n d B) = 0.12$

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) = 0.4 + 0.01 - (0.12)

$P (A \cup B) = 0.4 + 0.01 - (0.12)$

Step 3

Multiply

- 1

$- 1$ by

0.12

$0.12$ .

P (A \cup B) = 0.4 + 0.01 - 0.12

$P (A \cup B) = 0.4 + 0.01 - 0.12$

Step 4

Add

0.4

$0.4$ and

0.01

$0.01$ .

P (A \cup B) = 0.41 - 0.12

$P (A \cup B) = 0.41 - 0.12$

Step 5

Subtract

0.12

$0.12$ from

0.41

$0.41$ .

P (A \cup B) = 0.29

$P (A \cup B) = 0.29$

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