Chuck-a-Luck 博彩
Chuck a Luck
题目详情
一个博彩游戏：你可以花 1 卢比在 1~6 中选一个号码下注。随后掷 3 枚相同但可能不公平的骰子。
如果你下注的号码在 3 枚骰中出现了 0/1/2/3 次，你分别赢得 0/1/2/3 卢比（不返还下注的 1 卢比）。
问：买一张 1 卢比的票后，你的期望赢得金额是多少？
In this gambling game, a player can buy a ticket for Rs 1 on any number from 1 to 6. Three identical and unfair dice are rolled. If the booked number appears on 0, 1, 2 or 3 dice, player wins Rs 0, 1, 2 or 3 respectively, without returning the original Rs 1. What is expected money you can win after buying a ticket for Rs 1?
Hint
Book the full house
解析
期望赢得金额为 。
想法：把 1~6 每个号码都各买 1 张票（总花 6）。无论掷出什么点数，三枚骰子一共会给你返还 3（因为每个骰子点数对应的那张票返 1）。因此每张票的期望返还为 。
Original Explanation
1/2
Solution
We bet Rs 1 on each number 1-6. In any case, we get Rs 3 back. That is 1/2 per ticket. Hence the expected amount of money we can win is 1/2. A tedious way to arrive at this answer is to calculate the probability of getting 1, 2 or 3 faces common to our booking.