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You play the following game against your friend. You have two urns and three balls. One...

  • You play the following game against your friend. You have two urns and three balls. One of the balls is marked. You get to place the balls in the two urns any way you please, including leaving one urn empty. Your friend will choose one urn at random and then draw a ball from that urn. (If he chose an empty urn, there is no ball.) His goal is to draw the marked ball.

    1. How would you arrange the balls in the urns to minimize his chances of drawing the marked ball?  

    2. How would your friend arrange the balls in the urns to maximize his chances of drawing the marked ball?  

    3. Repeat (a) and (b) for the case of n balls with one marked ball.

Math   Statistics-And-Probability   
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Answer #1

Ans: in order to minimise his chances of drawing a marked ball, I will place all the 3 balls in any of the one urn and keep the other urn blank.

In order to maximise his chances of drawing a marked ball, I will place the marked ball in any of the one urn and keep the other 2 balls in other urn

In case of n balls,

In order to minimise his chance of drawing a marked ball, I will place all the n balls in any of the one urn and keep the other urn blank

In order to maximise his chance of drawing a marked ball, I will place the marked ball in any of the one urn and keep the n-1 balls in other urn

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