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# Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are

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Manager
Joined: 21 Jul 2003
Posts: 58
Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are  [#permalink]

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23 Jan 2010, 14:49
4
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:39) correct 11% (02:39) wrong based on 83 sessions

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Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?

A. 9/48
B. 9/20
C. 11/24
D. 27/48
E. 13/16
Intern
Joined: 21 Jan 2010
Posts: 48
Re: Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are  [#permalink]

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23 Jan 2010, 15:03
Mr. Yutaro’s class contains 5boys and 11 girls. If two students are chosen, one at a time, from the class, what is
the probability that a boy and a girl are chosen?
A. 9/48
B. 9/20
C. 11/24
D. 27/48
E. 13/16

Probability of a boy being chosen first, then a girl:
5/16 * 11/15

Probability of a girl being chosen first, then a boy:
11/16 * 5/15

Probability of a boy and a girl being chosen:
(5*11+5*11) / (15*16)
=11+11/3*16
=22/48
=11/24, so C.
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Joined: 15 Oct 2007
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Location: India
Re: Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are  [#permalink]

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19 Feb 2010, 04:40
(5C1*11C1)/16C2 = 11/24
Senior Manager
Joined: 21 Jul 2009
Posts: 327
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Re: Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are  [#permalink]

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19 Feb 2010, 11:24
1
umeshkathuria wrote:
(5C1*11C1)/16C2 = 11/24

Actually, problems of this kind, prefer subtracting from all possible probabilities = 1.

Subtract probability of choosing only two boys and probability of choosing only two girls and that should give the final answer. This will be more helpful when you have many more selections that happen and not just 2 and one from each is required.
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Joined: 01 Feb 2010
Posts: 233
Re: Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are  [#permalink]

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20 Feb 2010, 07:39
Mr. Yutaro’s class contains 5boys and 11 girls. If two students are chosen, one at a time, from the class, what is
the probability that a boy and a girl are chosen?
A. 9/48
B. 9/20
C. 11/24
D. 27/48
E. 13/16

Ways to choose one boy = 5c1 = 5
Ways to choose one girl = 11c1 = 11

Total ways = 16c2 = 16*15

p=(5*11)/16*15 - 11/24 hence C
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Re: Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are  [#permalink]

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28 Dec 2017, 15:32
Top Contributor
Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?

A. 9/48
B. 9/20
C. 11/24
D. 27/48
E. 13/16

P(1 boy and 1 girl chosen) = P(1st selection is boy AND 2nd selection is girl OR 1st selection is girl AND 2nd selection is boy)
= P(1st selection is boy AND 2nd selection is girl) + P(1st selection is girl AND 2nd selection is boy)
= P(1st selection is boy) x P(2nd selection is girl) + P(1st selection is girl) x P(2nd selection is boy)
= 5/16 x 11/15 + 11/16 x 5/15
= 55/240 + 55/240
= 110/240
= 11/24
= C

Cheers,
Brent
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Manager
Joined: 23 Oct 2017
Posts: 64
Re: Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are  [#permalink]

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28 Dec 2017, 18:10
Number of ways of selecting two students from the class of 5 boys & 11 girls = 16C2 (total) =15*16/2
Number of ways of selecting 1 boy & 1 girl = 5C1 * 11C1 = 5*11
probability = 5*11/15*8 = 11/24
Re: Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are &nbs [#permalink] 28 Dec 2017, 18:10
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