At the County Fair, you see a man sitting at a table and rapidly rolling a pea b

Question

At the County Fair, you see a man sitting at a table and rapidly rolling a pea between three walnut shells. "Step right up and try your luck! The hand is quicker than the eye!" he says, and hides the pea under one of the shells. You have no idea which shell is covering the pea, but you point to one shell at random and bet that the pea is under it. The man picks up one of the shells that you didn't choose, and shows you that the pea is not underneath that shell. He asks if you would like to switch your bet to the other unchosen shell. Should you accept the offer?

Explanation / Answer

probabilty of pea in your chosen shell=1/3

and in other shells =2/3

once he opens one shell out of them the probabilty to have pea in other shell will be 2/3

as probabilty of having pea in other shell is twice then in shell which you are holding

You shoud accept the offer

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