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# Sixty percent of the members of a university orchestra are seniors and

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
Sixty percent of the members of a university orchestra are seniors and  [#permalink]

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20 Mar 2018, 00:52
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Difficulty:

15% (low)

Question Stats:

81% (01:12) correct 19% (01:42) wrong based on 97 sessions

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Sixty percent of the members of a university orchestra are seniors and 45 percent of those seniors are in the university band. If one member of the university orchestra is randomly selected, what is the probability that the member is a senior band member?

(A) 0.15
(B) 0.27
(C) 0.30
(D) 0.45
(E) 0.75

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Posts: 58434
Re: Sixty percent of the members of a university orchestra are seniors and  [#permalink]

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20 Mar 2018, 00:55
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Sixty percent of the members of a university orchestra are seniors and  [#permalink]

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20 Mar 2018, 01:05
Bunuel wrote:
Sixty percent of the members of a university orchestra are seniors and 45 percent of those seniors are in the university band. If one member of the university orchestra is randomly selected, what is the probability that the member is a senior band member?

(A) 0.15
(B) 0.27
(C) 0.30
(D) 0.45
(E) 0.75

Out of 100 members of a university orchestra, 60 are seniors and 40 are juniors.

Since, 45% of the seniors are in the university band,
the number of seniors in the band are $$\frac{45}{100}*60 = \frac{9}{20}*60 = 27$$

Therefore, the probability that a member is a senior band member is $$\frac{27}{100}$$ = 0.27 (Option B)

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Re: Sixty percent of the members of a university orchestra are seniors and  [#permalink]

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21 Mar 2018, 08:21
60%of 45%of x=0.27x
p=0.27x/x=0.27
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Sixty percent of the members of a university orchestra are seniors and  [#permalink]

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22 Mar 2018, 18:33
Bunuel wrote:
Sixty percent of the members of a university orchestra are seniors and 45 percent of those seniors are in the university band. If one member of the university orchestra is randomly selected, what is the probability that the member is a senior band member?

(A) 0.15
(B) 0.27
(C) 0.30
(D) 0.45
(E) 0.75

The ratio of senior band member to total member: $$0.6*0.45 = 0.27$$
Therefore the probability that a randomly chosen member is a senior band member is $$0.27$$ (B)
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Posts: 3078
Re: Sixty percent of the members of a university orchestra are seniors and  [#permalink]

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26 Mar 2018, 10:01

Solution:

Given:

• Seniors in university orchestra = $$60%$$

• Seniors in university band = $$45%$$ of seniors in the orchestra

Working out:

We need to find that if a member is chosen from the university orchestra, what is the probability that he is a member of the university band.

Let there be $$100$$ members of the University orchestra.

From the question stem, we can infer that the number of seniors in this group = $$60% of 100 = 60$$

Seniors in university band = $$45%$$ of the seniors in the university orchestra = $$45% of 60 = 45*60 /100 = 27$$

P (Senior band member) = Ways to choose a senior band member / Ways to choose a member belonging to the university orchestra.

P (Senior band member) = $$27 / 100 = 0.27$$

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Re: Sixty percent of the members of a university orchestra are seniors and  [#permalink]

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05 Apr 2018, 11:09
Bunuel wrote:
Sixty percent of the members of a university orchestra are seniors and 45 percent of those seniors are in the university band. If one member of the university orchestra is randomly selected, what is the probability that the member is a senior band member?

(A) 0.15
(B) 0.27
(C) 0.30
(D) 0.45
(E) 0.75

We can let the number of members in the orchestra = 100.

So 60 seniors are in the orchestra, and 60 x 0.45 = 27 of those seniors are also in the band.

Thus, the probability of selecting a senior band member is 27/100 = 0.27.

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Re: Sixty percent of the members of a university orchestra are seniors and   [#permalink] 05 Apr 2018, 11:09
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