推 heyhey1025:哈哈 謝謝 我想的太複雜了 感謝感謝 03/29 17:58
※ 引述《heyhey1025 (heyhey)》之銘言：
: Suppose that a person plays a game in which his score must be one of the 5
: numbers 1,2...,5 and that each of these 5numbers is equally likely to be
: his score. The first time he plays the game, his score is X. He then
: continues to play the game until he obtains another score Y such that
: Y大於等於X. Assuming that all plays of the game are independent. Find the
: probability of the event that Y = 5
: 答案是137/300
: 請幫一下 謝謝
如果一開始抽到 1 (機率1/5)，之後抽到1～5都會結束遊戲，以5結束的機率是 1/5
如果一開始抽到 2 (機率1/5)，之後抽到2～5才能結束遊戲，以5結束的機率是 1/4
...
如果一開始抽到 5 (機率1/5)，只有之後抽到5才能結束遊戲，以5結束的機率是 1/1
1 1 1 1 1 1 137
- * [- + - + - + - + - ] = ---
5 5 4 3 2 1 300
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