Question

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? 0.20 0.55 0.60 0.80

Answer 1

The probability that students who were randomly selected studied for the test, if they pass it with a B or higher grade is: D. 0.80.

How to calculate the probability?

In this exercise, you're required to determine the probability that students who were randomly selected studied for the test, if they pass it with a B or higher grade. Thus, we would apply Bayes's theorem.

• Let S represent studied for.

• Let B represent a score of B or higher grade

Therefore, we need to find P(S|B):

$S|B = \frac{B|S \times S}{B|S \times S\; +\; B|S' \times S'} \\\\S|B = \frac{0.55 \times 0.6}{0.55 \times 0.6 \;+ \;0.2 \times 0.4}\\\\S|B =\frac{0.33}{0.33 + 0.08} \\\\S|B =\frac{0.33}{0.41}$

S|B = 0.80.

Read more on probability here: brainly.com/question/25870256

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Complete 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.