Finite Math Examples

$P (A) = 0.9$

Step 1

$A$ represents any event, and

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

$A$ and

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

$1$ . In this case,

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

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

Step 2

The probability of the complement event

$A'$ is

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

$1 - P A$ .

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

Step 3

Substitute the value of

$P (A)$ into

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

$P (A') = 1 - (0.9)$

Step 4

Multiply

$- 1$ by

$0.9$ .

$P (A') = 1 - 0.9$

Step 5

Subtract

$0.9$ from

$1$ .

$P (A') = 0.1$