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Regular Member
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引用:
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作者EraserFlying
原始題目，給個ａｎｓｗｅｒ 吧
Suppose you're on a game show, and you're given the choice of three doors; Behind one door is a car; behind the others, goats. You pick a door, say No.1 and the host, who knows what's behind the doors, opens another door, say No.3, which has a goat. He then says to you, "Do you want to pick door No.2?" Is it to your advantage to switch your choice?
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題目的兩面在於,如果玩這個遊戲要先付出$X的賭金,
當第一次選擇後,主持人開了一扇沒有獎金的門,
所以僅剩下兩個門,一個有$10K的獎金,另一個沒有任何獎賞,
而且規定你一定要有第二次選擇,
所以主持人會再給你一個機會讓你選擇,但不用再投入賭金
所以獎金的期望值為$10K*(1/2)=$5K,
如果賭金$X大於$5K則沒有玩的價值,
這個東西對於解釋原提意[換或不換]並沒有多大的關聯,主要是分析這個題目題意外的其他因素,
所以[2/3,1/3]是指已經開始玩這個遊戲的換與不換的中獎機率,而[1/2]是指整個遊戲的中獎機率 |