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. The probabilities are displayed in the tree diagram. A tree diagram. Random student studies for test is 0.6, and does not study for test is 0.4. Studies for test to Gets B or higher is 0.55; does not get B or higher is 0.45. Does not study for test to Gets B or higher is 0.20; does not get B or higher is 0.80. The professor informs the class that there will be a test next week. What is the probability that a randomly selected student passes the test with a B or higher?

Answer 1

Answer: 33%

Step-by-step explanation:

Probabilities are used to determine the chances of passing a test and getting a B grade

The probability that a selected student studies, and gets B or higher is 33%

Let the events be represented as follows:

A: The event that a student gets B or higher in a test if they study

B: The event that a student gets B or higher in a test if they do not study

So, we have:

60% of the students study.

So, the probability that a student studies, and gets B or higher is:

Substitute 55% for P(A)

Multiply

Express as percentage

Hence, the probability is 33%