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← Unit 6 · Addition rules

Lesson

Read the rule, then work each example: try the setup yourself, then tap to check one step at a time.

The rules

Mutually exclusive?

Mutually exclusive = no outcomes in common (they cannot both happen) → just add.

  1. Can one outcome be BOTH? (queen & diamond: yes — the Q♦).
  2. No → mutually exclusive: P(A or B) = P(A) + P(B). Grades B or C: .25 + .37 = .62.
  3. Yes → not mutually exclusive: subtract the overlap (next card).

Subtract the overlap once

P(A or B) = P(A) + P(B) − P(A and B); if B is inside A (red or heart), the answer is just P(A).

P(A or B) = P(A) + P(B) − P(A and B) (P(A ∪ B) = P(A) + P(B) − P(A ∩ B))

  1. Count A. Count B.
  2. Find the overlap: outcomes that are BOTH (the Q♥ and Q♦; the (4,4) roll; the Men-Yes cell).
  3. Add A + B, subtract the overlap ONCE.
  4. Two dice, double or sum 8: 6/36 + 5/36 − 1/36 = 10/36 = 5/18.
  5. Percents work the same way: male or under 18 = 76.2% + 15.3% − 10.8% = 80.7%.
Traps and calculator keys are on the unit page →

Worked examples (6)

Example 1 · 2.2 #1a0/4

Event A: Getting a queen. Event B: Getting a king

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Determine if the events are mutually exclusive.

Try the setup yourself first, then tap.

Example 2 · 2.2 #1b0/4

Event A: Getting a queen. Event B: Getting a diamond.

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Determine if the events are mutually exclusive.

Try the setup yourself first, then tap.

Example 3 · 2.2 #20/4

Records for one year show that 76.2% of the people arrested were male, 15.3% were under 18 years of age, and 10.8% were males under 18 years of age (published by the Federal Bureau of Investigation in Crime in the United States)
If a person arrested that year is selected at random, what is the probability that that person is either male or under 18?

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Try the setup yourself first, then tap.

Example 4 · 2.2 #3a0/4

a queen or a king

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A card is drawn from a standard 52-card deck, find the probability that the card is

Try the setup yourself first, then tap.

Example 5 · 2.2 #3b0/4

a queen or a diamond

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A card is drawn from a standard 52-card deck, find the probability that the card is

Try the setup yourself first, then tap.

Example 6 · 2.2 #3c0/4

a number less than 5 (ace, 2, 3, 4)

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A card is drawn from a standard 52-card deck, find the probability that the card is

Try the setup yourself first, then tap.

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