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# A certain class consists of 8 students, including Kim

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A certain class consists of 8 students, including Kim [#permalink]

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17 Feb 2012, 07:50
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Question Stats:

77% (02:09) correct 23% (01:31) wrong based on 216 sessions

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A certain class consists of 8 students, including Kim. 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 Kim 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

In solved in this way:

$$\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}$$

$$\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}$$

$$\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}$$

Therefore: $$\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = [m]\frac{3}{8}$$[/m]

Is there another way to solve it faster?

Source: Jeff Sackman questions - http://www.gmathacks.com
[Reveal] Spoiler: OA

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Re: A certain class consists of 8 students [#permalink]

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17 Feb 2012, 07:55
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metallicafan wrote:
A certain class consists of 8 students, including Kim. 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 Kim will be selected to complete one of the three tasks?

Since there are total of 8 students and we are selecting 3 of them, then the probability that Kim will be selected is simply 3/8 (she has 3 chances out of 8).

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Re: A certain class consists of 8 students [#permalink]

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17 Feb 2012, 08:12
Bunuel wrote:
metallicafan wrote:
A certain class consists of 8 students, including Kim. 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 Kim will be selected to complete one of the three tasks?

Since there are total of 8 students and we are selecting 3 of them, then the probability that Kim will be selected is simply 3/8 (she has 3 chances out of 8).

Thank you bunuel! However, I don't get your approach well. Could you explain your logic? I believe that the probability of picking somenone in the second task is different from picking someone in the first because the number of elements available to pick changes. That's why my approach is step by step.
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Re: A certain class consists of 8 students [#permalink]

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17 Feb 2012, 08:23
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metallicafan wrote:
Bunuel wrote:
metallicafan wrote:
A certain class consists of 8 students, including Kim. 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 Kim will be selected to complete one of the three tasks?

Since there are total of 8 students and we are selecting 3 of them, then the probability that Kim will be selected is simply 3/8 (she has 3 chances out of 8).

Thank you bunuel! However, I don't get your approach well. Could you explain your logic? I believe that the probability of picking somenone in the second task is different from picking someone in the first because the number of elements available to pick changes. That's why my approach is step by step.

The wording of the question makes it harder then it is. The question basically asks: what is the probability that Kim is among the first 3 students out of 8, which is 3/8.

One can also do: $$P=\frac{C^1_1*C^2_7}{C^3_8}=\frac{3}{8}$$, where $$C^1_1$$ is # of ways to select Kim, $$C^2_7$$ is # of ways to select any 2 students out of 7 left and $$C^3_8$$ is total # of ways to select 3 students from 8;

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

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

As you can see first approach is easiest and shortest one.

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Re: A certain class consists of 8 students, including Kim [#permalink]

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17 Feb 2012, 08:49
Thank you Bunuel!, I have updated the post with the choices.
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Re: A certain class consists of 8 students [#permalink]

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17 Feb 2012, 10:00
Thankx Bunuel, the explanation covers all possible ways of solving the problem
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Re: A certain class consists of 8 students, including Kim [#permalink]

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17 Feb 2012, 17:43
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One more way to sove this is to reverse the logic:
NOT chosen on first, second and third pick leads to the following calculation:
7/8 * 6/7 * 5/6 = 0,625. Since we are looking for the probability Kim gets chosen it's 1-0,625 = 0,375 = 3/8
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Re: A certain class consists of 8 students, including Kim [#permalink]

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23 Feb 2012, 10:06
I agree with B 3/8

third task = 7/8*6/7*1/6 = 1/8

chance that she gets picked for one of these is 1/8+1/8+1/8 or 3/8
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Re: A certain class consists of 8 students, including Kim [#permalink]

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22 Sep 2013, 10:33
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Re: A certain class consists of 8 students, including Kim [#permalink]

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03 May 2014, 23:35
metallicafan wrote:
A certain class consists of 8 students, including Kim. 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 Kim 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

In solved in this way:

$$\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}$$

$$\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}$$

$$\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}$$

Therefore: $$\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = [m]\frac{3}{8}$$[/m]

Is there another way to solve it faster?

Source: Jeff Sackman questions - http://www.gmathacks.com

Hello,

for completion of task B - why 7/8 * 1/7* 6/6??

for completion of task C - why 7/8 * 6/7* 1/6??

plx explain the one in BOLD especially..

Sharmita
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Re: A certain class consists of 8 students, including Kim [#permalink]

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04 May 2014, 03:01
Expert's post
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BOOKMARKED
msharmita wrote:
metallicafan wrote:
A certain class consists of 8 students, including Kim. 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 Kim 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

In solved in this way:

$$\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}$$

$$\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}$$

$$\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}$$

Therefore: $$\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = [m]\frac{3}{8}$$[/m]

Is there another way to solve it faster?

Source: Jeff Sackman questions - http://www.gmathacks.com

Hello,

for completion of task B - why 7/8 * 1/7* 6/6??

for completion of task C - why 7/8 * 6/7* 1/6??

plx explain the one in BOLD especially..

Sharmita

P(Kim)*P(any)*P(any) = $$\frac{1}{8} * \frac{7}{7} * \frac{6}{6} = \frac{1}{8}$$

P(any bu Kim)*P(Kim)*P(any) = $$\frac{7}{8} * \frac{1}{7} * \frac{6}{6} = \frac{1}{8}$$

P(any but Kim)*P(any but Kim)*P(any) = $$\frac{7}{8} * \frac{6}{7} * \frac{1}{6} = \frac{1}{8}$$

Faster solutions are here: a-certain-class-consists-of-8-students-including-kim-127730.html#p1046004 and here: a-certain-class-consists-of-8-students-including-kim-127730.html#p1046020

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Hope this helps.
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Re: A certain class consists of 8 students, including Kim [#permalink]

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01 Jun 2015, 15:22
Hello from the GMAT Club BumpBot!

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Re: A certain class consists of 8 students, including Kim   [#permalink] 01 Jun 2015, 15:22
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