HMMT 二月 2007 · 冲刺赛 · 第 6 题
HMMT February 2007 — Guts Round — Problem 6
题目详情
英文原题
- [ 6 ] There are three video game systems: the Paystation, the WHAT, and the ZBoz 2 π , and none ofthese systems will play games for the other systems. Uncle Riemann has three nephews: Bernoulli,
Galois, and Dirac. Bernoulli owns a Paystation and a WHAT, Galois owns a WHAT and a ZBoz 2 π , and
Dirac owns a ZBoz 2 π and a Paystation. A store sells 4 different games for the Paystation, 6 differentgames for the WHAT, and 10 different games for the ZBoz 2 π . Uncle Riemann does not understand the difference between the systems, so he walks into the store and buys 3 random games (not necessarilydistinct) and randomly hands them to his nephews. What is the probability that each nephew receivesa game he can play?
10 HARVARD-MIT MATHEMATICS TOURNAMENT, 24 FEBRUARY 2007 — GUTS ROUNDth
解析
英文解析
- [ 6 ] There are three video game systems: the Paystation, the WHAT, and the ZBoz 2 π , and none ofthese systems will play games for the other systems. Uncle Riemann has three nephews: Bernoulli,
Galois, and Dirac. Bernoulli owns a Paystation and a WHAT, Galois owns a WHAT and a ZBoz 2 π , and
Dirac owns a ZBoz 2 π and a Paystation. A store sells 4 different games for the Paystation, 6 differentgames for the WHAT, and 10 different games for the ZBoz 2 π . Uncle Riemann does not understand the difference between the systems, so he walks into the store and buys 3 random games (not necessarily 1
distinct) and randomly hands them to his nephews. What is the probability that each nephew receivesa game he can play?
Answer: . Since the games are not necessarily distinct, probabilities are independent. Multiplying 7
the odds that each nephew receives a game he can play, we get 10 / 20 · 14 / 20 · 16 / 20 = 7 / 25 .25
10 HARVARD-MIT MATHEMATICS TOURNAMENT, 24 FEBRUARY 2007 — GUTS ROUNDth