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

Question

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

amistre64 · Answer

what is our sample space of events?

amistre64 · Answer

study, and pass

or

not study, and pass

amistre64 · Answer

how do we calculate the probability of each event in the sample space?

kropot72 · Answer

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:
$$\large P(S\cap P)+P(NS \cap P)=you\ can\ calculate$$