What distribution should i use?

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Player1 is seeking to determine the expected number of players who will accept his bet, given the acceptance probabilities of three other players: 32%, 56%, and 20%. The assumption is that these probabilities remain constant regardless of prior acceptances. There is confusion regarding the outcome of the bet, as it is stated that only one player can win, yet multiple players can accept the bet. The average acceptance rate of the players is calculated to be 32% + 56% + 20%. The discussion emphasizes the need for clarity in understanding the betting dynamics and expected outcomes.
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Player1 makes the bet.
the 2nd player has a 32% chance to accept the bet.
the 3rd player has a 56% chance to accept the bet.
the 4th player has a 20% chance to accept the bet.

there can only be one winner of said bet, so player one is interested in knowing the EXPECTED number of players that will call his bet (how much competition will he have)

(we can make the assumption that the % chance of a player accepting the bet does not change depending on the # of players accepted before him..they aren't that smart)

anyone have an idea how I can approach this?

haven't taken stats in a while
 
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The question doesn't seem to be clear . I assume there are only 2 outcomes to a bet - win or lose . Now you say that no more than 1 player can win the bet , but how can that be :
If player 1 makes the bet , and then player 2 and player 3 accepts the bet , but player 4 declines .

If player 1 loses the bet then that means player 2 and 3 have won . But you said that no more than 1 player can win the bet. How come ?
 
The average number of players accepting the bet is 32% + 56% + 20%, of course.
 
CRGreathouse said:
The average number of players accepting the bet is 32% + 56% + 20%, of course.

lol so obvious i didnt notice.
 
rsala004 said:
lol so obvious i didnt notice.

...and that's what we're here for.
 

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