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:

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

Step-by-step 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.