A physics class has 40 students. Of these, 17 students are physics majors and 16 students are female. Of the physics majors, seven are female. Find the probability that a randomly selected student is female or a physics major.

Question

Mathematics

Giana Elliott

6 August, 23:34

A physics class has 40 students. Of these, 17 students are physics majors and 16 students are female. Of the physics majors, seven are female. Find the probability that a randomly selected student is female or a physics major.

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Answers (1)

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Mariyah Rocha · Answer 1

Probability of female P (f) = 0,575 or 57,5 %

Probability of physic majors P = 0,425 or 42,5 %

Step-by-step explanation:

a) Probability that a random selected student is female:

Let call P (f) such probability is P (f1) + P (f2)

we have to evaluate 2 branch of the tree, working as follows

1. Probability of students as physics major is P (f1)

17/40 and after that the probability of student physics majors being female is 7/17, Therefore for that side we have probability

P (f1) = (17/40) * (7/17) = 119/680

2.-Probability of students as female from 40 student is

16/40

Then P (f) = (119/680) + 16/40 P (f) = 391/680

P (f) = 0,575 or 57,5%

b) Probability of physics majosr is:

P (pm) = 17/40

P (pm) = 0,425 or 42,5 %