ANDREA IS A VERY GOOD STUDENT. THE PROBABILITY THAT SHE STUDIES AND PASSES HER MATHEMATICS TEST IS 17/20. IF THE PROBABILITY THAT ANDREA STUDIES IS 15/16, FIND THE PROBABILITY THAT ANDREA PASSES HER MATHEMATICS TEST, GIVEN THAT SHE HAS STUDIES.
Answer:
The probability that Andrea passes her mathematics test, given that she has studies is \(=\frac{68}{75}\)
Step-by-step explanation:
Given : Andrea is a very good student. The probability that she studies and passes her mathematics test is 17/20.If the probability that Andrea studies is 15/16.
To find : The probability that Andrea passes her mathematics test, given that she has studies ?
Solution:
Let A be the event that Andrea studies.
i.e, \(P(A)=\frac{15}{16}\) given.
Let B be the event that Andrea passes her mathematics test.
The probability that she studies and passes her mathematics test is
\(\text{P(A and B)}=\frac{17}{20}\)
Now, to find the probability that Andrea passes her mathematics test, given that she has studies \(P(B/A)\) is the conditional probability.
The formula to find probability is
\(P(B/A)=\frac{\text{P(A and B)}}{P(A)}\)
Substitute the values in the formula,
\(P(B/A)=\frac{\frac{17}{20}}{\frac{15}{16}}\)
\(P(B/A)=\frac{17\times 16}{15\times 20}\)
\(P(B/A)=\frac{272}{300}\)
\(P(B/A)=\frac{68}{75}/tex]
Therefore, The probability that Andrea passes her mathematics test, given that she has studies is [tex]=\frac{68}{75}\)