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5-55.

In a random sample of $10,000$ college students, a research company found that $35.7\%$ were involved in a club and $27.8\%$ studied $4$ or more hours per day. When they reported their findings, the research company indicated that $53.4\%$ of college students were either involved in a club or they studied $4$ or more hours per day. Given this information, what is the probability that a college student is involved in a club and studies $4$ or more hours per day? Homework Help ✎

Recall the Addition Rule. The Addition Rule is $P(\text{A or B)}=P(\text{A)}+P(\text{B)}−P(\text{A and B)}$.

$P(\text{students involved in a club)}+ P(\text{students studying more than 4 hours per day})$$- P(\text{students who perform either task)}=P(\text{students who do both)}$