Question

Giving a test to a group of students, the grades and gender are summarized below

	A	B	C	Total
Male	20	7	18	45
Female	5	17	15	37
Total	25	24	33	82

If one student is chosen at random,

Find the probability that the student was male:

Find the probability that the student was female AND got a "A":

Find the probability that the student was female OR got an "B":

Find the probability that the student was female GIVEN they got a 'A':

LicensePoints possible: 12

Answer 1

Giving a test to a group of students, the grades and gender are summarised below.

	A	B	C	Total
Male	20	7	18	45
Female	5	17	15	37
Total	25	24	33	82

Question a

We have to find the probability that a randomly selected student is male.

Now, we note that there are a total of 82 students, and 45 students are male among them.

So, the probability that a randomly selected student is male, is

=45/82

=0.5488.

Question b

We have to find the probability that a randomly selected student is female and got a A.

We note that there are 82 students in total, and among them there are 5 females who got a A.

So, the probability that a randomly selected student is female and got a A, is

=5/82

=0.0610.

Question c

We have to find the probability that a student was female or got a B.

Now, there are 82 students in total.

There are 37 females.

There are 24 students who got a B.

There are 17 students who got a B and are female.

So, the probability that a randomly selected student is female or got a B, is

=(37+24-17)/82

=44/82

=0.5366.

Question d

We have to find the probability that a student was female, given she got a A.

Now, there are 25 students who got a A.

Among them, 5 were females who got a A.

So, the probability that a randomly selected student was female, given they got a A, is

=P(Female|got A)

=P(Female and Got A)/P(Got A)

=(5/82)/(25/82)

=0.2.