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Question

In a group of students, the probability that they get greater than 90% on their statistics test is 0.42, the

probability that they slept at least 8 hours the night before the test is 0.516, the probability that they study with other classmates is 0.432, the probability that they get marks greater than 90% on their test and slept at least 8 hours the night before the test is 0.244, the probability that study with classmates and slept atl east 8 hours before the quiz is 0.166, they probability that they get marks greater than 90% on their test and study with classmates is 0.194, and probability that they do all three is 0.104.

Let A = getting greater than 90% on their test Let B = sleeping at least 8 hours Let C = studying with others

Determine the probability that a randomly selected student does not get greater than 90% and does not sleep at least 8 hours, given that you know they study with other classmates?

Answer 1

Make a Venn diagram and label the parts carefully

It should look like this graph in DESMOS: VENN01 (desmos.com)

You construct this using the data given in the problem by appropriate addition and subtraction.

Then you will see that the answer is .176/.432=.407