Question

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 1

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,

$P(B/A)=\frac{\frac{17}{20}}{\frac{15}{16}}$

$P(B/A)=\frac{17\times 16}{15\times 20}$

$P(B/A)=\frac{272}{300}$

$P(B/A)=\frac{68}{75}/tex]Therefore, The probability that Andrea passes her mathematics test, given that she has studies is [tex]=\frac{68}{75}$

Answer 2

Let B be the event that Andrea passes her test, and let A be the event 
that she studies. We are given that P(A and B) = 17/20, and that P(A) = 15/16. 

Now the probability that Andrea passes her test given that she has studied 
is represented by P(BlA). The formula your teacher gave you can be written as 
P(BlA) = P(A and B) / P(A). 

So P(BlA) = P(A and B) / P(A) = (17/20) / (15/16) = (17/20)*(16/15) = 68/75.