A teacher designs a test so a student who studies will pass 85% of the time, but a student who does not study will pass 11% of the time. A certain student studies for 86% of the tests taken. On a given test, what is the probability that student passes? FINITE MATH

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A teacher designs a test so a student who studies will pass 85% of the time, but a student who does not study will pass 11% of the time. A certain student studies for 86% of the tests taken. On a given test, what is the probability that student passes? FINITE MATH

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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what is our sample space of events?
study, and pass or not study, and pass
how do we calculate the probability of each event in the sample space?

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Other answers:

This can be solved by the use of a probability tree: |dw:1443932148840:dw| \[\large P(S \cap P)=0.86\times0.85\] \[\large P(NS \cap P)=0.14\times0.11\] The required probability is therefore given by: \[\large P(S\cap P)+P(NS \cap P)=you\ can\ calculate\]

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