Answer: [tex]\dfrac{4}{7}[/tex]
Step-by-step explanation:
Given : Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 8 10 7 25
Female 6 13 14 33
Total 14 23 21 58
Total students = 58
Total number of students got A = 14
P(students got A) [tex]=\dfrac{14}{58}[/tex]
Total number of students got A and not female = 8
P( students got A and not female ) = [tex]\dfrac{8}{58}[/tex]
Now , By conditional probability ,
P(NOT a female | got a "A" ) = [tex]\dfrac{\text{P( students got A and not female )}}{\text{P(students got A)}}[/tex]
[tex]=\dfrac{\dfrac{8}{58}}{\dfrac{14}{58}}\\\\=\dfrac{8}{14}=\dfrac{4}{7}[/tex]
∴ The probability that the student was NOT a female that got a "A" is [tex]\dfrac{4}{7}[/tex] .
