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2 years ago

9

8. At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance the

y 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?
A. 0.20
B. 0.55
C. 0.60
D. 0.80

1 answer:

Bezzdna [24]2 years ago

3 0

Answer:

.8

Step-by-step explanation:

S= studies for

B= score of b or higher

we want P(S|B)

Using Bayes' theorem we can solve for the probability

$S|B=\frac{B|S*S}{B|S*S+B|S'*S'}=\frac{.55*.6}{.55*.6+.2*.4}=0.80487804878$

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