A school has to send the report cards of 3 students, but the clerk has not paid attention to match the address on the envelope with the student report card. The probability that exactly one of the students received his or her own report card is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{2} \)
The 3 report cards can go into the 3 envelopes in 3! = 6 equally likely ways.
For exactly one student to get the right card, that student can be chosen in 3 ways; the other two cards must then both be wrong, which happens in only 1 way (they are interchanged).
\( \displaystyle \text{Favourable ways}=3\times 1=3 \)
\( \displaystyle P(\text{exactly one correct})=\frac{3}{6}=\frac{1}{2} \)
Check by listing, with students 1, 2, 3 and cards in that order: 123 (all correct), 132, 213, 321 (exactly one correct each), 231, 312 (none correct).