Question

Use 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

First break down the counts:
- A only = 15 − 6 = 9
- B only = 10 − 6 = 4
- A ∩ B = 6
- Outside = 4
Total = 9 + 6 + 4 + 4 = 23.

So
- P(A) = 15/23
- P(B) = 10/23
- P(A|B) = P(A ∩ B)/P(B) = 6/10 = 3/5
- P(B|A) = 6/15 = 2/5

None of the four given equalities is correct.