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## Homework Statement

high school has 417 students total

186 of total are athletes (play sports)

136 of total are musicians (play music)

74 of total are musicians and athletes. (play music and play sports)

a) at which probability does randomly chosen athlete also play music (i.e. be a musician)

b) at which probability does randomly chosen student play sports or play music.

## Homework Equations

## The Attempt at a Solution

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I think we are given the condition that the student must be an athlete in the beginning.

There are only 186 athletes in the school it seems.

Therefore those athletes who are also musicians. They are 74 in number

Therefore the probability = 74/186

roughly 40%. I wonder if this is the correct method though.

there are overall 417 students. It should be noted that there exist students there, who are neither athletes nor are the musicians. Maybe they are in the debate club. etc...

the randomly chosen student can be

- non-participant in sports and music
- pure athlete
- pure musician
- athlete-musician

IF the student is (athlete-musician) or (athlete) or (musician) then the condition for event is favorable and fulfilled indeed.

It looks like probability for student is therefore = (186+136-74)/ 417

=248/417

roughly 59%

the probability for non-participant = 1- (248/417) =41%