problem 4. a player plays a game where she is equally likely to win or lose 1 dollar. the games are independent. the player will c

Question

problem 4. a player plays a game where she is equally likely to win or lose 1 dollar. the games are independent. the player will continue playing until the first win occurs and then stop immediately after. (a) find the probability that her winnings are greater than zero. (b) find the probability that her winnings are less than zero. (c) find the expected value of her winnings.

Eirian · Answer

We get  (A) The  probability  that her  winnings  will exceed zero is 0.50.  (B) The probability that her winnings will be less than zero is 0.25.  (c) Her winnings' estimated worth is 0.    Given that,  A player engages in a  game  where the odds of winning or losing one dollar are  equal . The games are stand-alone. The game will be played until the first win occurs, at which point the player will instantly stop.  We have to find  (A) determine the probability that her winnings will exceed  zero .  (B) calculate the probability that her winnings will be less than zero.  (c) calculate her winnings' estimated worth.  We know that,  a) probability that her winnings are greater than zero =P(wins 1st game) =1/2 =  b) probability that her winnings are less than zero =P(lose 1st 2 games) =(1/2)×(1/2 )=1/4 =0.25  c) below is pmf of X ( gain  from the game)  P(X=1)=P(win 1st game) =1/2  P(X=0)=P(lose 1st and win 2nd) =(1/2)×(1/2) =1/4  P(X=-1)=P(lose 1st two and wins 3rd)=(1/2)×(1/2)×(1/2) =1/8  P(X=-2)=1/16  therefore expected value E(X )=ΣxP(x) =1×1/2+0×1/4-1×1/8-2×1/16........   = (1/2)+0-(1×1/8+2×1/16+3×1/32+4×1/64+...)  =(1/2)-(1/4)×(1/(1/2))  =(1/2)-(1/2)  =0  Therefore,   (A) The probability that her winnings will exceed zero is 0.50.  (B) The probability that her winnings will be less than zero is 0.25.  (c) Her winnings' estimated worth is 0.    To learn more about  probability  visit: https://brainly.com/question/11234923  #SPJ4

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