Statistics Examples

P (A) = 0.64

$P (A) = 0.64$ ,

P (B) = 0.22

$P (B) = 0.22$ ,

P (A o r B) = 0.86

$P (A o r B) = 0.86$

Step 1

A

$A$ and

B

$B$ are mutually exclusive events if they cannot occur at the same time. For example, tossing a coin once results in either head or tail, but not both. The probability of their joint occurrence is zero

P (A \cap B) = 0

$P (A \cap B) = 0$ and it is not possible for

A

$A$ and

B

$B$ to be independent because

P (A | B) = P (B | A) = 0

$P (A | B) = P (B | A) = 0$ for mutually exclusive

A

$A$ and

B

$B$ .

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

$P (A \cup B) = P (A) + P (B)$ for mutually exclusive events

Step 2

Add

0.64

$0.64$ and

0.22

$0.22$ .

P (A) + P (B) = 0.86

$P (A) + P (B) = 0.86$

Step 3

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

$P (A \cup B) = P (A) + P (B)$ , which means that

A

$A$ and

B

$B$ are mutually exclusive events.

A and B are mutually exclusive events

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