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

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Manager
Joined: 26 Dec 2018
Posts: 142
Location: India
Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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01 Jan 2019, 18:09
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

77% (02:17) correct 23% (01:54) wrong based on 61 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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Manager
Joined: 01 May 2017
Posts: 82
Location: India
Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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Updated on: 10 Jan 2019, 02:41
3
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, 18:37.
Last edited by Dare Devil on 10 Jan 2019, 02:41, edited 1 time in total.
Intern
Joined: 18 Jul 2018
Posts: 6
Re: Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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09 Jan 2019, 22:21
Any more explanations for this question would be appreciated?

Thanks so much.
Intern
Joined: 16 Dec 2018
Posts: 10
Re: Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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09 Jan 2019, 22:33
1
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
Intern
Joined: 27 Jan 2017
Posts: 30
Re: Alan and Becky are among the ten students a teacher can choose from to  [#permalink]

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10 Jan 2019, 00:37
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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
Re: Alan and Becky are among the ten students a teacher can choose from to   [#permalink] 10 Jan 2019, 00:37
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