Statistics Examples

P (A) = 0.69

$P (A) = 0.69$

Step 1

A

$A$ represents any event, and

A'

$A'$ is the complement of that event. Combined, the mutually exclusive events

A

$A$ and

A'

$A'$ represent every possible outcome in the sample space, so the sum of their two probabilities adds to

1

$1$ . In this case,

P (A) + P (A') = 1

$P (A) + P (A') = 1$ .

P (A) + P (A') = 1

$P (A) + P (A') = 1$

Step 2

The probability of the complement event

A'

$A'$ is

P (A')

$P (A')$ , which is equal to

1 - P A

$1 - P A$ .

P (A') = 1 - P A

$P (A') = 1 - P A$

Step 3

Substitute the value of

P (A)

$P (A)$ into

P (A') = 1 - P A

$P (A') = 1 - P A$ .

P (A') = 1 - (0.69)

$P (A') = 1 - (0.69)$

Step 4

Multiply

- 1

$- 1$ by

0.69

$0.69$ .

P (A') = 1 - 0.69

$P (A') = 1 - 0.69$

Step 5

Subtract

0.69

$0.69$ from

1

$1$ .

P (A') = 0.31

$P (A') = 0.31$

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