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

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards