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%
<em><u>A - The proportion of students that like trance music but not dubstep is:</u></em>
P(T) - P(D and T)=25%-15%=10%
<u><em>B - The proportion of students that like either dubstep or trance is:</em></u>
P(D) + P(T) - P(D and T) =30%+25%-15% = 40%
<u><em>C - The proportion of students that like neither trance music nor dubstep is</em></u>
100% - (P(D) + P(T) - P(D and T) ) =60%
<u><em>D - The proportion of students that didn’t select any of the music options available on the survey was:</em></u>
100% - (P(H)+P(D) + P(T) - P(D and T) ) =40%
<u><em>F - The conditional probability that a student likes dubstep, given that he or she likes trance music, is:</em></u>
=
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