There are 90 students in our Foundation program. All of these take some combination of Maths, Chemistry or Biology. The number who take Chemistry is 44; the number who take Biology is 50; and 50 take Maths. The number who take Maths and Biology is 20; the number who take Chemistry and Biology is 24, and there are 20 who take Maths only and 15 who take Biology only. a) Find the probability that a student picked at random studies only Chemistry. b) Find the probability that a student picked at random studies all three courses. c) Find the probability that a student picked at random studies Chemistry given that the student is studying Maths.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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please can you explain how they came up with the van diagram middle numbers such as 11,9,10 and 15. 

Question 3
Part 1:
ml=50
20
10
10
9
15
15
Bl=50
ID
cl= 44
Transcribed Image Text:Question 3 Part 1: ml=50 20 10 10 9 15 15 Bl=50 ID cl= 44
Part 1:
There are 90 students in our Foundation program. All of these take some combination of
Maths, Chemistry or Biology. The number who take Chemistry is 44; the number who take
Biology is 50; and 50 take Maths. The number who take Maths and Biology is 20; the number
who take Chemistry and Biology is 24, and there are 20 who take Maths only and 15 who take
Biology only.
a) Find the probability that a student picked at random studies only Chemistry.
b) Find the probability that a student picked at random studies all three courses.
c) Find the probability that a student picked at random studies Chemistry given that the
student is studying Maths.
Transcribed Image Text:Part 1: There are 90 students in our Foundation program. All of these take some combination of Maths, Chemistry or Biology. The number who take Chemistry is 44; the number who take Biology is 50; and 50 take Maths. The number who take Maths and Biology is 20; the number who take Chemistry and Biology is 24, and there are 20 who take Maths only and 15 who take Biology only. a) Find the probability that a student picked at random studies only Chemistry. b) Find the probability that a student picked at random studies all three courses. c) Find the probability that a student picked at random studies Chemistry given that the student is studying Maths.
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