Students in a school were surveyed about their study habits. Forty-two percent of students said they study on weeknights and weekends, 47% said they studied on weekends, and 65% said they study either on weeknights or weekends. If you were to pick one student at random, what is the probability that he or she studies on a weeknight?40%60%45%50%
Question
Students in a school were surveyed about their study habits. Forty-two percent of students said they study on weeknights and weekends, 47% said they studied on weekends, and 65% said they study either on weeknights or weekends. If you were to pick one student at random, what is the probability that he or she studies on a weeknight?40%60%45%50%
Solution
The problem can be solved using the principle of Inclusion and Exclusion.
According to the problem,
P(Weeknights U Weekends) = P(Weeknights) + P(Weekends) - P(Weeknights ∩ Weekends)
We know that,
P(Weeknights U Weekends) = 65% (Probability that a student studies either on weeknights or weekends)
P(Weekends) = 47% (Probability that a student studies on weekends)
P(Weeknights ∩ Weekends) = 42% (Probability that a student studies on both weeknights and weekends)
We need to find P(Weeknights) (Probability that a student studies on weeknights)
Substituting the known values in the equation, we get
65% = P(Weeknights) + 47% - 42%
Solving for P(Weeknights), we get
P(Weeknights) = 65% - 47% + 42% = 60%
So, the probability that a student studies on a weeknight is 60%.
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