A class in advanced physics consists of 10 juniors, 30 seniors, and 10 graduate

Question

A class in advanced physics consists of 10 juniors, 30 seniors, and 10 graduate students. The final grades show that 3 of the juniors, 10 of the seniors and 5 of the graduate students received an "A" for the course. The gender (Male/Female) composition of the class is one to three across the board. a. What is the sample space of this probability problem? b. Convert the data to a tabular format If a student is chosen at random from this class, and is found to have an "A", what is the probability the she/he is a senior? c. d. Suppose the randomly selected student is a male. What is the probability of him being from the junior class? (20 points)

Explanation / Answer

a)

Here the sample space consists of 50 students

b)

A not A Total

Junior 3 7 10

Senior 10 20 30

Graduate 5 5 10

Total 18 32 50

c)

P(Senior | A) = P(Senior and A)/P(A)

= 10/18

= 0.5556

d)

P(Junior | Male) = P(Junior and Male)/P(Male)

n(Junior and Male) = 1/4*10 = 2.5

n(Male) = 1/4*50 = 12.5

P(Junior | Male) = 2.5/12.5 = 0.2

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