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

Answer 1

what is our sample space of events?

Answer 2

study, and pass

or

not study, and pass

Answer 3

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

Answer 4

This can be solved by the use of a probability tree:

\[\large P(S \cap P)=0.86\times0.85\]
\[\large P(NS \cap P)=0.14\times0.11\]
The required probability is therefore given by:
\[\large P(S\cap P)+P(NS \cap P)=you\ can\ calculate\]