Respuesta :
Answer:
The probability that Andrea passes her mathematics test, given that she has studies is [tex]=\frac{68}{75}[/tex]
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, [tex]P(A)=\frac{15}{16}[/tex] given.
Let B be the event that Andrea passes her mathematics test.
The probability that she studies and passes her mathematics test is
[tex]\text{P(A and B)}=\frac{17}{20}[/tex]
Now, to find the probability that Andrea passes her mathematics test, given that she has studies [tex]P(B/A)[/tex] is the conditional probability.
The formula to find probability is
[tex]P(B/A)=\frac{\text{P(A and B)}}{P(A)}[/tex]
Substitute the values in the formula,
[tex]P(B/A)=\frac{\frac{17}{20}}{\frac{15}{16}}[/tex]
[tex]P(B/A)=\frac{17\times 16}{15\times 20}[/tex]
[tex]P(B/A)=\frac{272}{300}[/tex]
[tex]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}[/tex]
