## Two students $$A$$ and $$B$$ participate in Physics and Chemistry exams. Each exam subject has $$6$$ different exam code

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### Two students $$A$$ and $$B$$ participate in Physics and Chemistry exams. Each exam subject has $$6$$ different exam code

by AAPL » Thu Feb 08, 2024 4:59 pm

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## Global Stats

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 a random 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. $$1/36$$

OA D

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### Re: Two students $$A$$ and $$B$$ participate in Physics and Chemistry exams. Each exam subject has $$6$$ different exam

by mapadvantageprep » Fri Feb 16, 2024 10:23 am
The second student has a 1/6 chance to match the same code in Physics as the first student and a 5/6 chance not to match the same code in Chemistry.
Now, let's calculate the probability that the second student has the same code in Physics but not in Chemistry:
Probability of same code in Physics but not in Chemistry
=1/6 × 5/6
Probability of same code in Physics but not in Chemistry= 5/36

Similarly, the probability that the second student has the same code in Chemistry but not in Physics:
Probability of same code in Chemistry but not in Physics =5/6 ×1/6
Probability of same code in Chemistry but not in Physics= 5/36

Therefore, the total probability is the sum of these two probabilities:
Total probability
5/36 + 5/36
= 10/36
= 5/18

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