The game of Match is played with a special deck of 27 cards. Each card has three attributes: color, shape and number. The possible color values are {red, blue, green}, the possible shape values are {square, circle, heart}, and the possible number values are {1, 2, 3}. Each of the 3*3*3 = 27 possible combinations is represented by a card in the deck. A match is a set of 3 cards with the property that for every one of the three attributes, either all the cards have the same value for that attribute or they all have different values for that attribute. For example, the following three cards are a match: (3, red, square), (2, blue, square), (1, green, square).
1. If we shuffle the deck and turn over three cards, what is the probability that they form a match? Hint: given the rest two cards, what is the probability that the third forms a match?
2. If we shuffle the deck and turn over n cards where n≤27, what is the expected number of matches, where we count each match separately even if they overlap? Note: The cards in a match do not need to be adjacent! Is your expression correct for n= 27?

第二题没看懂啊，第一题是1/25吧

twhdong 发表于 2012-8-30 17:19
第二题没看懂啊，第一题是1/25吧

额 说说过程啊。。。

先申明一下，第一题应该是3/25，第一个题提示很明显了，先固定前两张，对于这两张的三个参数，每一组，无论是不同还是相同，第三张在同一位置的数都确定了，也就是说当前两张确定时，最后能成组的一张也就确定了，而其他的都不能成组，总共27张，出去前两张，最后也就剩25张，只有1张能行，算式（27*26*1/2!）/(27*25*26/3!),也就是3/25
第二题，个人英语水品有限，没有看懂题目啊