Question

a researcher randomly selected 132 high school students and asked them about their study habits and lighting preference when studying. the two-way table displays the data. suppose one of the students is randomly selected. let \\(l\\) = the student prefers low light and \\(s\\) = the student sometimes studies.

which of the following is the correct value and interpretation of \\(p(s|l)\\)?

• \\(p(s|l) = 0.57\\); given that the student prefers low light, there is a 0.57 probability that they sometimes study.
• \\(p(s|l) = 0.35\\); given that the student prefers low light, there is a 0.35 probability that they sometimes study.
• \\(p(s|l) = 0.57\\); given that the student sometimes studies, there is a 0.57 probability that they prefer low light.
• \\(p(s|l) = 0.35\\); given that the student sometimes studies, there is a 0.35 probability that they prefer low light.

Explanation:

Calculate the conditional probability

$$ P(S|L) = \frac{P(S \cap L)}{P(L)} = \frac{21}{37} \approx 0.57 $$

Interpret the conditional probability

$$ \text{Given that the student prefers low light (L), the probability that they sometimes study (S) is } 0.57. $$

Answer:

• (A) \(P(S|L) = 0.57\); given that the student prefers low light, there is a 0.57 probability that they sometimes study. (Correct answer)
• (B) \(P(S|L) = 0.35\); given that the student prefers low light, there is a 0.35 probability that they sometimes study.
• (C) \(P(S|L) = 0.57\); given that the student sometimes studies, there is a 0.57 probability that they prefer low light.
• (D) \(P(S|L) = 0.35\); given that the student sometimes studies, there is a 0.35 probability that they prefer low light.