Consider the following game between the card dealer and yourself. There are thre

Question

Consider the following game between the card dealer and yourself.

There are three cards - two marked zero, and one marked 1 (prize). These cards are put on the table upside-down (you cannot see the numbers).

Clearly, if you just given a choice to select one out of three cards, then the probability to win the prize is 1/3 and the game is not fair.

You propose a modified strategy -

1. You select a card, but don’t look at it

2. After you’ve selected a card, the dealer looks at the two remaining cards and removes one card which contains 0 (i.e. does not contain the prize).

3. You’re given a choice to either keep the card you selected previously or to switch to the one which remains on the table.

4. Show that the winning strategy is to always switch the card, i.e. to take the card which remains on the table, and compute the probability to win the prize under this strategy.

Explanation / Answer

probabilty that you old the winning card =1/3

and probabilty that the lot of 2 cards which is with dealer contain winning card =2/3

hence once dealer remove a losing card from his lot probabilty of winning from remaining card remain 2/3

therefore it is always better to switch the card and probabilty to win the prize under this strategy =2/3

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