Question

Mr. Connor's physics class has 102102 students, classified by academic year and gender, as illustrated in the table. Mr. Connor randomly chooses one student to collect yesterday's work.

Mr. Connor's Physics Class

Academic Year	Males	Females
Freshmen	9	12
Sophomores	19	9
Juniors	19	7
Seniors	17	10

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Step 1 of 2:

What is the probability that he selects a female, given that he chooses randomly from only the sophomores? Express your answer as a fraction or a decimal rounded to four decimal places.

Answer 1

Mr. Conor's Physics class has 102 students. The students are classified as follows.

Academic Year	Males	Females	Total
Freshmen	9	12	21
Sophomores	19	9	28
Juniors	19	7	26
Seniors	17	10	27
Total	64	28

Now, we have to find the probability that he selects a female, given that he chooses randomly from only the sophomores.

So, we have to find

=

First we find

Now, all possible cases is 102. And there are 19+9, ie. 28 sophomores.

So,

=

Now, we have to find

Now, again all possible cases is 102. And there are only 9 students who are both female and sophomores.

So,

=

So,

=

=

=

=

So, the probability that Mr. Conor selects a female, given that he chooses randomly only from the sophomores is 0.3214.