The addition rule and mutually exclusive events

Three quick questions from earlier lessons.

In a deck of 52 cards, 13 are hearts and 4 are kings. How many cards are a heart or a king?

Add, then remove the overlap.

General addition rule:

P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)

. If

A

and

B

are mutually exclusive (cannot both happen),

P(A \text{ and } B) = 0

and

P(A \text{ or } B) = P(A) + P(B)

.

P(heart or king).

\tfrac{13}{52} + \tfrac{4}{52} - \tfrac{1}{52}

Each part.

= \tfrac{16}{52} = \tfrac{4}{13}

Simplify.

Your turn: P(A) = 0.5, P(B) = 0.4, P(A and B) = 0.2. Find P(A or B).

0.7

0.5 + 0.4 − 0.2.

In a class of 35 students, 12 are girls, 12 play soccer and 2 girls play soccer. A student is chosen at random. Find P(girl or soccer player).
In a class of 34 students, 16 are girls, 10 play soccer and 4 girls play soccer. A student is chosen at random. Find P(girl or soccer player).
In a class of 35 students, 19 are girls, 8 play soccer and 4 girls play soccer. A student is chosen at random. Find P(girl or soccer player).

Events A and B are mutually exclusive, with P(A) = 0.31 and P(B) = 0.24. Find P(A and B).

A spinner lands on red with probability 0.21 and on blue with probability 0.32. Find P(red or blue).

Three questions to check you have got it.

In a class of 35 students, 12 are girls, 12 play soccer and 2 girls play soccer. A student is chosen at random. Find P(girl or soccer player).
In a class of 34 students, 16 are girls, 10 play soccer and 4 girls play soccer. A student is chosen at random. Find P(girl or soccer player).
In a class of 35 students, 19 are girls, 8 play soccer and 4 girls play soccer. A student is chosen at random. Find P(girl or soccer player).

Addition rule

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$ ; for disjoint events the last term is 0.

Watch out: disjoint is not the same as independent.

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