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At a certain school 25% of the students join a band...

by swerve » Wed Mar 14, 2018 1:30 pm
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

The OA is E.

Can I solve this PS question as follow?

Students joined band = 25%.
Students in both 20%.

20/25 = 4/5. Option E.
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by Jay@ManhattanReview » Thu Mar 15, 2018 9:31 pm
swerve 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

The OA is E.

Can I solve this PS question as follow?

Students joined band = 25%.
Students in both 20%.

20/25 = 4/5. Option E.
Yes, you got it correct.

The selected student also plays Sport given that he is a member of the band, means that he belongs to both = 20%

We know that 25% students are members of the band

Probability = (The percentage of students belongs to both) / (The percentage of students joined band) = 20%/25% = 4/5.

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Mon Mar 19, 2018 3:35 pm
swerve 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.

Answer: E

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by deloitte247 » Sun Apr 01, 2018 8:10 am
Of all the students in the school,
$$25\%\ join\ a\ band$$
$$25\%\ play\ a\ sport$$
$$20\%\ join\ the\ band\ and\ play\ a\ sport$$
Therefore, probability that a student selected at random is a member of the band and also play a sport
$$=\frac{\left(no.\ of\ required\ outcomes\right)}{no.\ of\ possible\ outcomes}=\frac{20\%}{100\%}$$
$$=\frac{1}{5}\ \left(option\ B\right)$$
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