In a group of 800 people, 1/5 play at least one instrument..

Question

In a group of 800 people, 1/5 play at least one instrument, 96 play two or more. What is the probability that one student play exactly one instrument?

A) 2/125
B) 3/125
C)2/25
D) 3/25
E) 1/5

Bunuel · Answer

Given that 1/5*800=160 students play 1 or more instrument and 96 play 2 or more, so 160-96=64 students play exactly 1 instrument.

Therefore the probability that a randomly chosen student plays exactly one instrument is 64/800=2/25.

Answer: C.

EvaJager · Answer

P(playing 2 or more instruments) = 96/800 = 3/25. 
Then, the probability of playing exactly one instrument is given by:
P(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 3/25 = 2/25.

Answer C.

Bunuel · Answer

Bumping for review and further discussion.

rever08 · Answer

Given that 1/5*800=160 students play 1 or more instrument

96 play 2 or more,

Therefore, 160-96=64 students play exactly 1 instrument.

Therefore, the probability that a randomly chosen student plays exactly one instrument is 64/800=2/25.

Poorvasha · Answer

1/5th of the 800 students play at least one instrument = 1/5*800 = 160
96 played two or more.
No of students that played exactly one = 160-96= 64

P(E)= 64/160 = 2/25 (C)

Princ · Answer

OA:C

No. of Students play 1 instrument +No. of Students play 2 instruments +No. of Students play 3 instruments +................... = \frac{1}{5}*800 =160

No. of Students play 2 instrument +No. of Students play 3 instruments +No. of Students play 4 instruments +................... = 96

No of Student play exactly 1 instrument  = 160-96=64

probability that one student play exactly one instrument  = \frac{64}{800}=\frac{2}{25}

ScottTargetTestPrep · Answer

We see that 1/5 x 800 = 160 people play at least one instrument.

Since 96 people play two or more instruments, then 160 - 96 = 64 play exactly one.

So the probability that a student plays exactly one instrument is 64/800 = 8/100 = 2/25.

Answer: C

Kinshook · Answer

Given: In a group of 800 people, 1/5 play at least one instrument, 96 play two or more.

Asked: What is the probability that one student play exactly one instrument?

Total students = 800
Students playing at least one instrument = 800/5 = 160
Students playing two or more instruments = 96
Students playing only one instrument = 160 - 96 = 64

The probability that one student play exactly one instrument = 64/800 = 2/25

IMO C

bumpbot · Answer

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In a group of 800 people, 1/5 play at least one instrument..

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