A group of college DJs surveyed students to find out what music to plan for thei

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. The proportion of students that didn't select any of the music options available on the survey was: 0%. 20%. 60%. 40%.
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. The proportion of students that didn't select any of the music options available on the survey was: 0%. 20%. 60%. 40%.

Explanation / Answer

A->Dubstep, B->Trance, C->House

Given P(A)=0.3, P(B)=0.25, P(C)=0.2, P(A^B)=0.15

P(AUBUC)=0.3+0.25+0.2-0.15=0.6

Hence P(Didnt select)=1-P(AUBUC)=1-0.6=0.4

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