Problem Solving

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

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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