A teacher designs a test so a student who studies will pass 90% of the time, but a student who does not studywill pass 5% of the time. A certain student studies for 93% of the tests taken. On a given test, what is theprobability that student passes? Round to the nearest thousandth when necessary.
A) 0.841
B) 0.837
C) 0.475
D) 0.035

Question

Quizplus · Accepted Answer

The probability that the student passes is calculated by considering both scenarios: studying and not studying. The probability of passing after studying is 0.90, and the probability of the student studying is 0.93, so the combined probability for this scenario is 0.90 * 0.93. The probability of passing without studying is 0.05, and the probability of not studying is 0.07 (100% - 93%), so the combined probability for this scenario is 0.05 * 0.07. Adding these two probabilities gives the overall probability of passing: (0.90 * 0.93) + (0.05 * 0.07) = 0.837 + 0.0035 = 0.8405, which rounds to 0.841.

A Teacher Designs a Test So a Student Who Studies