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At a certain school 25% of the students join a band, 25% play a sport

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Intern
Joined: 03 Jan 2011
Posts: 10
At a certain school 25% of the students join a band, 25% play a sport  [#permalink]

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06 Nov 2011, 22:48
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Difficulty:

45% (medium)

Question Stats:

61% (01:51) correct 39% (01:32) wrong based on 44 sessions

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At a certain school 25% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probability that the student also plays a sport?

A. 3/4
B. 1/5
C. 2/5
D. 1/2
E. 4/5

I chose 2) 1/5 which is wrong. I took the 20% ( who play the sport and join the band ).
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Re: At a certain school 25% of the students join a band, 25% play a sport  [#permalink]

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06 Nov 2011, 23:12
This is the way to approach the question:
25% of the students join a band => 25% of the students either only join a band or both join a band and play sports
25% of the students play sports => 25% of the students either only play sports or both play sports and join a band

If a randomly selected student is a member of the band, then probability that the student also plays a sport = percentage of cases in which the student can do both/percentage of cases in which the student can just play sports or do both
=20%/25% = 4/5

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Intern
Joined: 23 Nov 2009
Posts: 12
Re: At a certain school 25% of the students join a band, 25% play a sport  [#permalink]

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07 Nov 2011, 13:20
shinna wrote:
At a certain school 25% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probablility that the student also plays a sport?

1) 3/4
2)1/5
3)2/5
4)1/2
5)4/5

I chose 2) 1/5 which is wrong. I took the 20% ( who play the sport and join the band ).

students joined band = 25%
students in both 20%

20/25 = 4/5
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Re: At a certain school 25% of the students join a band, 25% play a sport  [#permalink]

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07 Nov 2011, 18:11
Number of students in band is 25%. 20% of them are also in sports. Probability is 20/25 = 4/5.
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Re: At a certain school 25% of the students join a band, 25% play a sport  [#permalink]

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19 Mar 2018, 16:22
shinna wrote:
At a certain school 25% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probability that the student also plays a sport?

A. 3/4
B. 1/5
C. 2/5
D. 1/2
E. 4/5

We can let the number of students = 100.

We know that 25 join the band, 25 play a sport and 20 do both.

We are told that a randomly selected student is a band member, so we consider only the 25 students who are band members. Of those 25, we know that 20 play a sport. Thus, the probability that a student plays a sport, given that he joins a band is 20/25 = 4/5.

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Re: At a certain school 25% of the students join a band, 25% play a sport   [#permalink] 19 Mar 2018, 16:22
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