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We probably have played the game "Throwing Balls into the Basket". It is a simple game. We have to throw a ball into a basket from a certain distance. One day we were playing the game. But it was slightly different from the main game.

In our game we were $N$ people trying to throw balls into $M$ identical Baskets. At each turn we all were selecting a basket and trying to throw a ball into it. After the game we saw exactly $S$ balls were successful. Now I will be given the value of $N$ and $M$. For each player probability of throwing a ball into any basket successfully is $P$.

Assume that there are infinitely many balls and the probability of choosing a basket by any player is $1/M$. If multiple people choose a common basket and throw their ball, we can assume that their balls will not conflict, and the probability remains same for getting inside a basket. I have to find the expected number of balls entered into the baskets after $K$ turns.

My question is that how can I find out the expected number? I'm a novice in learning the expected value. Therefore, better explanation is crying need for me.

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  • $\begingroup$ is this homework? if so please tag $\endgroup$ – chuse Jan 29 '15 at 16:03
  • $\begingroup$ I don't understand something: you didn't know N,M before playing? How many balls each player plays per turn, only one? if so, and the probabilities do not depend on the basket, and the balls do not interfere, the expected value is just KpN, K times the expected value of one turn. $\endgroup$ – chuse Jan 29 '15 at 16:08

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