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Alan and Becky are among the ten students a teacher can choose from to

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Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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New post 01 Jan 2019, 17:09
1
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (01:55) correct 27% (00:57) wrong based on 41 sessions

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Alan and Becky are among the ten students a teacher can choose from to form a six-student team. If all six students are chosen at random, what is the probability of choosing a team that includes Alan and Becky?

A. 1/9
B. 1/6
C. 2/9
D. 5/18
E. 1/3

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Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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New post Updated on: 10 Jan 2019, 01:41
2
1
Alan and Becky can be chosen in 2C2 combinations = C(2,2) = 1

Remaining 4 can be chosen in 8C4 combinations = C(8,4)
= 70

Alan, Becky with 4 other forming the team possibility = 70*1
= 70

Total combinations of a team of 6 out of 10 = C(10,6)
= 210

probability of choosing a team that includes Alan and Becky = 70/210
=1/3

Originally posted by Dare Devil on 01 Jan 2019, 17:37.
Last edited by Dare Devil on 10 Jan 2019, 01:41, edited 1 time in total.
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Re: Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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New post 09 Jan 2019, 21:21
Any more explanations for this question would be appreciated?

Thanks so much.
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Re: Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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New post 09 Jan 2019, 21:33
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All six students have the equal probability(ie, 1/6).

In that probability of choosing alan and becky is 1/6+1/6 =1/3.

Posted from my mobile device
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Re: Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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New post 09 Jan 2019, 23:37
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HarikaBurlakanti wrote:
All six students have the equal probability(ie, 1/6).

In that probability of choosing alan and becky is 1/6+1/6 =1/3.

Posted from my mobile device


Not sure that logic is correct. In probabilities when there is an "and" it requires multiplication.

Think of it as a Draft.

Round 1: There is a 6/10 chance Alan is picked.

Round 2: There is a 5/9 chance Becky is picked. (The pool has become smaller)

Combined probability = 6/10 * 5/9 = 30/90 = 1/3
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Re: Alan and Becky are among the ten students a teacher can choose from to &nbs [#permalink] 09 Jan 2019, 23:37
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Alan and Becky are among the ten students a teacher can choose from to

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