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.