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Forty percent of students belong to a club, 50 percent work part time and five percent do both. What is the probability of belonging to a club given part time work?
AThe probability is 0.05
BThe probability is 0.10
CThe probability is 0.40
DThe probability is 0.13
Answer & Solution
Correct answer: B. The probability is 0.10
1. The conditional is the joint probability divided by the probability of the condition.
2. That gives 0.05 divided by 0.50.
3. The result is 0.10, so only one in ten part time workers belongs to a club.
4. Since 0.10 is well below the club membership rate of 0.40, the two events are far from independent.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.5 Venn Diagrams_
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