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):
[tex]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}[/tex]
S|B = 0.80.
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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.
