Question

se the Venn diagram to calculate probabilities.

Circles A and B overlap. Circle A contains 15, circle B contains 10, and the intersection contains 6. Number 4 is outside of the circles.

Which probability is correct?

P(A) = Three-fifths
P(B) = StartFraction 16 Over 31 EndFraction
P(A|B) = Two-sevenths
P(B|A) = StartFraction 10 Over 21 EndFraction

Answer 1

Interpret the diagram as A-only = 15, B-only = 10, A∩B = 6, outside = 4. Total N = 15+10+6+4 = 35.

Compute:
- |A| = 15+6 = 21 → P(A) = 21/35 = 3/5 (correct).
- |B| = 10+6 = 16 → P(B) = 16/35 (not 16/31).
- P(A|B) = |A∩B|/|B| = 6/16 = 3/8 (not 2/7).
- P(B|A) = |A∩B|/|A| = 6/21 = 2/7 (not 10/21).

So only P(A) = 3/5 is correct.