HMMT 十一月 2012 · 冲刺赛 · 第 20 题
HMMT November 2012 — Guts Round — Problem 20
题目详情
英文原题
- [ 11 ] An elementary school teacher is taking a class of 20 students on a field trip. To make sureher students don’t get lost, she uses the buddy system—using the complete class roster, she pairs thestudents into 10 pairs and leaves if no person reports that someone from his or her pair is missing. Inparticular, the teacher will not notice if both students from a pair go missing. Suppose each studentindependently gets lost with probability . Given that the teacher leaves, what is the probability that 1
no student got lost?10
解析
英文解析
- [ 11 ]
8110
Answer: The teacher will leave if the students from each pair are either both present or both
8210
not present; the probability that both are present is and the probability that neither are present 81
1100
is . If the teacher leaves, then the probability that both students in any given pair did not get lost
( )100
8110
81 81 8110
is = . Since there are ten pairs, the overall probability is = .100
81 1
82 82 8210
100 100+