Answer:
The probability that Andrea passes her mathematics test, given that she has studies is 
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,
given.
Let B be the event that Andrea passes her mathematics test.
The probability that she studies and passes her mathematics test is

Now, to find the probability that Andrea passes her mathematics test, given that she has studies
is the conditional probability.
The formula to find probability is

Substitute the values in the formula,



![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}](https://tex.z-dn.net/?f=P%28B%2FA%29%3D%5Cfrac%7B68%7D%7B75%7D%2Ftex%5D%3C%2Fp%3E%3Cp%3E%3Cstrong%3ETherefore%2C%20The%20probability%20that%20Andrea%20passes%20her%20mathematics%20test%2C%20given%20that%20she%20has%20studies%20is%3C%2Fstrong%3E%20%5Btex%5D%3D%5Cfrac%7B68%7D%7B75%7D)