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

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AAPL: Moderator; Posts: 2706; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Thu Feb 08, 2024 4:59 pm

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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 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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Source: Beat The GMAT — Problem Solving | Thu Feb 08, 2024 4:59 pm

mapadvantageprep: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Tue Feb 13, 2024 8:47 am

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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