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 $1$ .

$P (A') = 0.1$