Question

A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance.
A - The proportion of students that like trance music but not dubstep is:

a) 20% .

b) 5% .

c) 10% .

d) 15%

B - The proportion of students that like either dubstep or trance is:

a) 40% .

b) 100% .

c) 55% .

d) 70% .

C - The proportion of students that like neither trance music nor dubstep is:

a)60% .

b) 20% .

c) 0% .

d) 40% .

D - The proportion of students that didn’t select any of the music options available on the survey was:

a) 0% .

b) 40% .

c) 20% .

d) 60% .

E - The proportion of students that preferred either dubstep or trance is calculated by:

a) P(A)+P(B)+P(A and B) .

b) None of the answer options are correct.

c) P(A)+P(B) .

d) P(A)+P(B)?P(A and B) .

F - The conditional probability that a student likes dubstep, given that he or she likes trance music, is:

a) 70% .

b) 65% .

c) 60% .

d) 55% .

Answer 1

Answer:

A - The proportion of students that like trance music but not dubstep is 10%

B - The proportion of students that like either dubstep or trance is 40%

C - The proportion of students that like neither trance music nor dubstep is 60%

D - The proportion of students that didn’t select any of the music options available on the survey was 40%

E - The proportion of students that preferred either dubstep or trance is calculated by: P(D) + P(T) - P(D and T)

F - The conditional probability that a student likes dubstep, given that he or she likes trance music, is 60%

Step-by-step explanation:

P(D)=the students preferred dubstep=30%

P(T)=the students selected trance music=25%

P(H)=the students selected house music=20%

P(D and T)=the students liked both dubstep and trance=15%

A - The proportion of students that like trance music but not dubstep is:

P(T) - P(D and T)=25%-15%=10%

B - The proportion of students that like either dubstep or trance is:

P(D) + P(T) - P(D and T) =30%+25%-15% = 40%

C - The proportion of students that like neither trance music nor dubstep is

100% - (P(D) + P(T) - P(D and T) ) =60%

D - The proportion of students that didn’t select any of the music options available on the survey was:

100% - (P(H)+P(D) + P(T) - P(D and T) ) =40%

F - The conditional probability that a student likes dubstep, given that he or she likes trance music, is:

$\frac{P(D and T)}{P(T)}$ =$\frac{0.15}{0.25} =0.60$