A teacher designs a test so that 92% of students who study will pass and 7% of students who don't study will pass.94% of students study for a test.What is the probability that a randomly selected student passes?
A)0.042
B)0.869
C)0.865
D)0.92
E)0.495

Question

Quizplus · Accepted Answer

The probability that a student passes can be calculated using the total probability theorem. Let's denote S as the event of a student studying and S' as not studying. P(Pass) = P(Pass|S)P(S) + P(Pass|S')P(S'). Given P(Pass|S) = 0.92, P(S) = 0.94, P(Pass|S') = 0.07, and P(S') = 0.06 (since 1 - 0.94 = 0.06), we get P(Pass) = 0.92*0.94 + 0.07*0.06 = 0.8648 + 0.0042 = 0.869.

A Teacher Designs a Test So That 92% of Students