Question

At CPP, the probability that a randomly chosen student is female is 0.45, the probability that the student is a business major is 0.20, and the probability that the student is female and a business major is 0.09. Use this information, answer the following questions: (a) What is the probability that the student is female or a business major? (4 points) (b) What is the probability that the student is female given that the student is a business major? (4 points) (c) What is the probability that the student is a business major given that the student is female? (4 points) (d) Are the events “female” and “business major” independent? Explain. (4 points) (e) Are the events “female” and “business major” mutually exclusive? Explain. (4 points)

Answer 1

(there are more than 4 parts, but i'll answer all 5, PLEASE UPVOTE)

F = female

B = business major

P(F)=0.45

P(B)=0.20

P(F,B) = 0.09

a.

P(F or B) = P(F) + P(B) - P(F,B)

= 0.45 + 0.20 - 0.09

= 0.56

probability that the student is female or a business major = 0.56

b.

P(F | B) = P(F,B) / P(B)

= 0.09/0.20 = 0.45

probability that the student is female given that the student is a business major = 0.45

c.

P(B | F) = P(F,B) / P(F)

= 0.09/0.45 = 0.20

probability that the student is a business major given that the student is female = 0.20

d.

for independence :

P(F,B) = P(F)*P(B)

P(F)*P(B) = 0.45*0.2 = 0.09 = P(F,B)

therefore ,

P(F,B) = P(F)*P(B)

so,

events “female” and “business major” are independent

e.

for mutually exclusive :

P(F,B) has to be 0

but P(F,B) = 0.09 is given

therefore, events “female” and “business major” are not mutually exclusive

(please UPVOTE)