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 \(\frac{2\times 6 \times 1 \times 6 \times 5}{6 \times 6 \times 6 \times 6}=\frac{5}{18}\)
The answer is D
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