Question

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.

Answer 1

Answer:

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 %