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

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Joined: 30 Jun 2012
Posts: 7
In a group of 800 people, 1/5 play at least one instrument..  [#permalink]

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Updated on: 05 Aug 2012, 15:58
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:30) correct 21% (01:38) wrong based on 246 sessions

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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

Originally posted by ferrarih on 05 Aug 2012, 07:00.
Last edited by ferrarih on 05 Aug 2012, 15:58, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 50711
Re: In a group with 800 people...  [#permalink]

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05 Aug 2012, 07:08
1
1
ferrarih wrote:
In a grouup of 800 people, 1/5 play at least one instrument, 96 play two or more. Whats it is e probability that one student play exactly one instrument?

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

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.

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Re: In a group with 800 people...  [#permalink]

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05 Aug 2012, 07:14
ferrarih wrote:
In a grouup of 800 people, 1/5 play at least one instrument, 96 play two or more. Whats it is e probability that one student play exactly one instrument?

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

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.

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Posts: 50711
Re: In a group of 800 people, 1/5 play at least one instrument..  [#permalink]

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13 Jul 2013, 23:11
Bumping for review and further discussion.
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Re: In a group of 800 people, 1/5 play at least one instrument..  [#permalink]

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15 Sep 2017, 09:44
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.
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Posts: 73
Re: In a group of 800 people, 1/5 play at least one instrument..  [#permalink]

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15 Sep 2017, 11:36
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)
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In a group of 800 people, 1/5 play at least one instrument..  [#permalink]

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24 Oct 2018, 07:34
1
ferrarih wrote:
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

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 $$= \frac{64}{800}=\frac{2}{25}$$
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Re: In a group of 800 people, 1/5 play at least one instrument..  [#permalink]

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25 Oct 2018, 16:53
ferrarih wrote:
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

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.

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Re: In a group of 800 people, 1/5 play at least one instrument.. &nbs [#permalink] 25 Oct 2018, 16:53
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