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?

Answer 1

Answer: 60% joaobezerra Is Right, and Confirmed by Buzz (Acceleration Education)

Explanation:

We solve this question by treating these events as Venn probabilities. Forty-two percent of students said they study on weeknights and weekends. This means that 47% said they studied on weekends. This means that 65% said they study either on weeknights or weekends. This is If you were to pick one student at random, what is the probability that he or she studies on a weeknight?

0.6 = 60% that he or she studies on a weeknight.

Answer 2

0.6 = 60% probability that he or she studies on a weeknight.

Explanation:

We solve this question treating these events as Venn probabilities.

I am going to say that:

Probability A: Probability of a student studying on weeknights.

Probability B: Probability of a student studying on weekends.

Forty-two percent of students said they study on weeknights and weekends

This means that
`P(A \cap B) = 0.42`

47% said they studied on weekends

This means that
`P(B) = 0.47`

65% said they study either on weeknights or weekends.

This is
`P(A \cup B) = 0.65`

If you were to pick one student at random, what is the probability that he or she studies on a weeknight?

This is P(A), and the equation used is:

`P(A \cup B) = P(A) + P(B) - P(A \cap B)`

Considering the values we have:

`0.65 = P(A) + 0.47 - 0.42`

`0.05 + P(A) = 0.65`

`P(A) = 0.6`

0.6 = 60% probability that he or she studies on a weeknight.