Answer:
p(w) = p = 1/1000 = 0.001
q = 1-p = 0.999
reward for winning = 600$
payoff for attempt = 0.6$
a.
on an avg. jose loose 0.4$ per hand,
so equation will be to find out one win per x hands,
-0.4 x = -0.6x + 600
so x = 3000.
Hence 1 win out of 3000,
P(losing 0.4$) = \binom{3000}{1}(0.001)^1(0.999)^{2999}
P(losing 0.4$) = 0.1492
b.
Probability of winning 0.4$ per winning
equation,
0.4 x = -0.6x + 600
so ,
x = 600
so out of 600 game he have to win 1 game.
P(winning 0.4$) = \binom{600}{1}(0.001)^1(0.999)^{599}
P(winning 0.4$) = 0.3295
c.
Probability of winning 0.6$ per winning
equation,
0.6 x = -0.6x + 600
so ,
x = 500
so out of 500 game he have to win 1 game.
P(winning 0.6$) = \binom{500}{1}(0.001)^1(0.999)^{499}
P(winning 0.6$) = 0.3034
Attached is the same solutions incase the above isn't understandable.
