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Two students A and B participate in Physics and Chemistry exams. Each

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Bunuel
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Two students A and B participate in Physics and Chemistry exams. Each [#permalink] New post   22 Jan 2020, 02:15
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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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Re: Two students A and B participate in Physics and Chemistry exams. Each [#permalink] New post   22 Jan 2020, 02:19
Expert Reply
Bunuel 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


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Total Combinations of exam codes = 6 (choices of Physics exam code)*6 (choices of Physics exam code) = 36

Required Probability = (36/36)*(1/36) = 1/36

Answer: Option E
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Re: Two students A and B participate in Physics and Chemistry exams. Each [#permalink] New post   22 Jan 2020, 03:27
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Bunuel 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


Required Probability = (same code in Physics & different code in Chemistry) or (same code in Chemistry & different code in Physics)

Probability of both getting same code in physics = Probability of both getting same code in chemistry = \(\frac{6}{6}*\frac{1}{6} = \frac{1}{6}\) [1st person can get from any 6 codes & 2nd person has to get exact code]
Probability of both getting different code in physics = Probability of both getting different code in chemistry = \(\frac{6}{6}*\frac{5}{6} = \frac{5}{6}\) [1st person can get from any 6 codes & 2nd person has to get from remaining 5 codes]

--> Required Probability = \(\frac{1}{6}*\frac{5}{6} + \frac{1}{6}*\frac{5}{6} = \frac{5}{36} + \frac{5}{36} = \frac{10}{36} = \frac{5}{18}\)

Option D
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Re: Two students A and B participate in Physics and Chemistry exams. Each [#permalink] New post   24 Jan 2020, 10:34
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Bunuel 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


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Let’s say the first student already has two codes: one for Physics and the other for Chemistry. The second student has ⅙ chance to match the same code in Physics as the first student and ⅚ chance not to match the same code Chemistry. Therefore, the second student has ⅙ x ⅚ = 5/36 chance to have the same code in Physics but not in Chemistry. Using the same logic, we can see that he will also has 5/36 chance to have the same code in Chemistry but not in Physics. Therefore, the probability is 5/36 + 5/56 = 10/36 = 5/18.

Answer: D
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Re: Two students A and B participate in Physics and Chemistry exams. Each [#permalink] New post   16 Apr 2024, 11:15
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Re: Two students A and B participate in Physics and Chemistry exams. Each [#permalink]
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