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.

the professor informs the class that there will be a test next week. what is the probability that a randomly selected student studied for the test if they pass it with a b or higher?

• 0.60
• 0.80
• 0.20
• 0.55

Explanation:

Define events and given probabilities

$$
LATEXBLOCK0
$$

Calculate the total probability of getting a B or higher

$$
LATEXBLOCK1
$$

Calculate the conditional probability of studying given a B or higher

$$
LATEXBLOCK2
$$

Answer:

• (A) 0.60
• (B) 0.80 (Correct answer)
• (C) 0.20
• (D) 0.55