Question

at the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a b or higher on the tests. if they do not study, there is a 20% chance that they will get a b or higher on the tests. the professor knows from prior surveys that 60% of students study for the tests. what is the probability that a randomly selected student studies for a test and gets a b or higher? 0.08 0.11 0.33 0.55

Explanation:

Step1: Identify the probabilities

Let \(P(S)\) be the probability that a student studies (\(P(S)=0.6\)), and \(P(B|S)\) be the probability of getting a B or higher given that a student studies (\(P(B|S) = 0.55\)).

Step2: Use the formula for joint probability

The formula for joint probability is \(P(S\cap B)=P(S)\times P(B|S)\).
Substitute the values: \(P(S\cap B)=0.6\times0.55\).
Calculate \(0.6\times0.55 = 0.33\).

Answer:

0.33