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# A certain class consists of 8 students, including Don. Each

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Status: Preparing for GMAT - March 2011
Joined: 21 May 2010
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WE 1: Finance 6 years
A certain class consists of 8 students, including Don. Each [#permalink]

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01 Mar 2011, 04:39
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Difficulty:

35% (medium)

Question Stats:

65% (01:23) correct 35% (00:53) wrong based on 37 sessions

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A certain class consists of 8 students, including Don. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Don will be selected to complete one of the three tasks?

A. 1/3
B. 3/8
C. 1/24
D. 1/336
E. 1/512
[Reveal] Spoiler: OA

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Re: word problem - Probability [#permalink]

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01 Mar 2011, 04:47
$$\frac{1}{8}*1*1 + \frac{7}{8}*\frac{1}{7}*1+\frac{7}{8}*\frac{6}{7}*\frac{1}{6}$$

$$3*\frac{1}{8} = \frac{3}{8}$$

Ans: "B"
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Re: word problem - Probability [#permalink]

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01 Mar 2011, 06:18
Expert's post
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tirupatibalaji wrote:
A certain class consists of 8 students, including Don. Each day, three tasks must be completed and are assigned as follows: one of the 8 students is selected at random to complete Task A, one of the remaining 7 students is selected at random to complete Task B, and one of the remaining six students is selected at random to complete Task C. What is the probability that Don will be selected to complete one of the three tasks?
(A) 1/3
(B) 3/8
(C) 1/24
(D) 1/336
(E) 1/512

Alternately you can find the probability that among 3 students chosen to complete the tasks won't be Don and subtract it from 1:
$$P=1-\frac{C^3_7}{C^3_8}=\frac{3}{8}$$;

The same with probability approach: $$P=1-\frac{7}{8}*\frac{6}{7}*\frac{5}{6}=\frac{3}{8}$$.

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Re: word problem - Probability [#permalink]

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01 Mar 2011, 06:21
P(don will not be selected to complete any) = (1 - 1/8) (1 - 1/7) (1 - 1/6) = 5/8

P(don will be selected atleast once) = 1 - 5/8 = 3/8
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Re: word problem - Probability [#permalink]

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01 Mar 2011, 07:14
2
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Expert's post
There's no need for a complicated solution here. We're selecting 3 people from 8 and we want to know the probability Don is selected. That's just like lining the 8 people up, and asking the probability Don is one of the first 3 people in line. There are 8 spots for Don, 3 of which are among the first three spots, so the probability must be 3/8.

edit - Or to look at it a different way, each of the 8 people is as likely as anyone else to be selected for A, for B, or for C. That is, the probability Don is selected for A is 1/8, for B is also 1/8 and for C is 1/8, so the probability he is selected for one of the three is 1/8 + 1/8 + 1/8 = 3/8.
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Re: A certain class consists of 8 students, including Don. Each [#permalink]

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05 Apr 2018, 23:19
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A certain class consists of 8 students, including Don. Each   [#permalink] 05 Apr 2018, 23:19
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