The probability that a student who has an A is a female is 3/8
How to calculate the probability of an event?
Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
What is chain rule in probability?
For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is probability of occurrence of A given that B already occurred.
We're specified a frequency table as:
Female Male
Has an A 3 5
Does not have an A 8 13
We want to get P(Student is female if its given that student has an A).
Symbolically, we need P(Female | Has an A).
P(Student is female | Student has an A) = P(Student is female ∩ Student has an A) / P(Student has an A)
Now, P(Student is female ∩ Student has an A) = n(Student is female∩ Student has an A) / n(all type of students) = 3/(3+5+8+13) = 3/29
Also, P(Has an A) = n(has an A)/ n (All type of students) = n(has an A)/29
Since n(has an A) = number of students having A = females having A + males having A = 3+5 = 8
Thus, P(Has an A) = 8/29
Thus, we get:
P(Female | Has an A) = P(Female ∩ Has an A) / P(Has an A) = [tex]\dfrac{3/29}{8/29} = \dfrac{3}{8}[/tex]
Thus, the probability that a student who has an A is a female is 3/8
Learn more about probability here:
brainly.com/question/1210781
