Unit 6 · 2.2

Addition rules

Mutually exclusive → add; otherwise subtract the overlap once

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Rule cards

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

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

Traps

Mixed up mutually exclusive and independent.
coin and die can happen together → mutually exclusive
✓ mutually exclusive = cannot happen at the same time (queen & king; head & tail)
Subtracted an overlap that does not exist.
queen or jack → 4/52 + 4/52 − 1/52
✓ no card is both → 8/52 = 2/13

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))

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

Traps

Added without removing the double-counted outcomes.
queen or red → 4/52 + 26/52 = 30/52
✓ 4/52 + 26/52 − 2/52 = 28/52 = 7/13 (exam Q20)
Removed the overlap two times.
4 + 13 − 1 − 1
✓ 6 or spade: 4 + 13 − 1 = 16/52 = 4/13
Multiplied for an OR question.
queen or red → 4/52 × 26/52
✓ OR → add, then subtract the overlap
Used a row total as the denominator in a table OR question.
P(man OR read) = (785 + 1100 − 534)/785
✓ the base is the grand total: 1351/1520 = 89%