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# Two students A and B participate in Physics and Chemistry exams

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Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
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Two students A and B participate in Physics and Chemistry exams  [#permalink]

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30 Nov 2016, 08:57
1
6
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Difficulty:

65% (hard)

Question Stats:

53% (02:27) correct 47% (02:13) wrong based on 116 sessions

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Two students A and B participate in Physics and Chemistry exams. Each exam subject has 6 different exam codes and two exam subjects have their own different exam codes. In each exam subject, each student receives randomly exam code. What is the probability that A and B receive the same exam code in only one subject?

A. 7/18
B. 4/9
C. 2/9
D. 5/18
E. 1/36

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Senior CR Moderator
Status: Long way to go!
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Posts: 1392
Location: Viet Nam
Re: Two students A and B participate in Physics and Chemistry exams  [#permalink]

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04 Dec 2016, 03:55
1
nguyendinhtuong wrote:
Two students A and B participate in Physics and Chemistry exams. Each exam subject has 6 different exam codes and two exam subjects have their own different exam codes. In each exam subject, each student receives randomly exam code. What is the probability that A and B receive the same exam code in only one subject?

A. 7/18
B. 4/9
C. 2/9
D. 5/18
E. 1/36

Re-edited the question because of typing mistake.
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Two students A and B participate in Physics and Chemistry exams  [#permalink]

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05 Dec 2016, 19:14
1
1
3
nguyendinhtuong wrote:
Two students A and B participate in Physics and Chemistry exams. Each exam subject has 6 different exam codes and two exam subjects have their own different exam codes. In each exam subject, each student receives randomly exam code. What is the probability that A and B receive the same exam code in only one subject?

A. 7/18
B. 4/9
C. 2/9
D. 5/18
E. 1/36

Solution.

Assume that Physics exam has 6 exam codes 1, 2, 3, 4, 5, 6
Chemistry exam has 6 exam codes 7, 8, 9, 10, 11, 12.

In each exam, A and B could receive 6 different exam codes. Hence, total selections are 6*6*6*6

In case that A and B receive the same exam code only in Physics exam.
In Physics exam, A could receive 6 different codes from 1 to 6. Since B receive the same code as A, B could receive only 1 code.
In Chemistry exam, A could receive 6 different codes from 7 to 12. B could receive the 5 remaining codes.

Hence, the total selections are 6*1*6*5.

Likewise, the total selections in the case that A and B receive the same exam code only in Chemistry exam are 6*1*6*5.

Hence, the total selections that A and B receive the same exam code only in one exam are 2*6*1*6*5.

The probability is $$\frac{2\times 6 \times 1 \times 6 \times 5}{6 \times 6 \times 6 \times 6}=\frac{5}{18}$$

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Posts: 32
Re: Two students A and B participate in Physics and Chemistry exams  [#permalink]

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06 Dec 2016, 02:25
Please explain why is it multiplied with 2.
thanks
Senior CR Moderator
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Two students A and B participate in Physics and Chemistry exams  [#permalink]

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06 Dec 2016, 02:38
sanaexam wrote:
Please explain why is it multiplied with 2.
thanks

In case that A and B have the same code in Physics and have different codes in Chemistry, the selections are 6*1*6*5
In case that A and B have the same code in Chemistry and have different codes in Physics, the selections are 6*1*6*5
Hence, the total selections are 6*1*6*5 + 6*1*6*5 = 2*6*1*6*5
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Joined: 19 Sep 2016
Posts: 8
Re: Two students A and B participate in Physics and Chemistry exams  [#permalink]

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31 Dec 2016, 04:18
1
This is how I decided to solve it:
Lets say A already got his exam codes. So, total combinations for B are 6x6
For B to get same exam code in exactly one subject, he should get different code in physics and same in chemistry or same in physics and different in chemistry
so 5C1 x 1C1 + 1C1 x 5C1 = 10
Hence, probability = 10/36 = 5/18
Manager
Joined: 24 Oct 2016
Posts: 81
GMAT 1: 670 Q46 V36
Two students A and B participate in Physics and Chemistry exams  [#permalink]

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10 Aug 2018, 17:49
broall wrote:
Two students A and B participate in Physics and Chemistry exams. Each exam subject has 6 different exam codes and two exam subjects have their own different exam codes. In each exam subject, each student receives randomly exam code. What is the probability that A and B receive the same exam code in only one subject?

A. 7/18
B. 4/9
C. 2/9
D. 5/18
E. 1/36

Easy Way:

Match: Physics x No Match: Chem
(1*1/6)x(1*5/6) = 5/36
Match: Chem x No Match: Physics
(1*1/6)x(1*5/6) = 5/36

Ans = 5/36 * 2 = 5/18
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