b Given that the student selected is a senior what is the pr

(b) Given that the student selected is a senior, what is the probability that she is also a physics major?

Total = 48 students

Seniors = 24

Physics majors = 29

Neither seniors nor physics majors = 7

So, seniors or physics majors = 48 - 7 = 41

P(senior or physics major) = P(senior) + P(physics major) - P(senior and physics major)

41 = 24 + 29 - x

41 = 53 - x

x = 53 - 41

x = 12 ---> ANSWER

So, we have 12 people who are both senior and a physics major....

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P(physics major | senior) = P(physics major and senior) / P(senior)

= 12 / 24

= 1/2 --> ANSWER