SOLUTION: A man wins a gambling game iif he gets two heads in five flips of a biased coin. The probability of getting a head with the coin is 0.7. a)find the probability the man will win. S

Algebra ->  Probability-and-statistics -> SOLUTION: A man wins a gambling game iif he gets two heads in five flips of a biased coin. The probability of getting a head with the coin is 0.7. a)find the probability the man will win. S      Log On


   

Question 327963: A man wins a gambling game iif he gets two heads in five flips of a biased coin. The probability of getting a head with the coin is 0.7.
a)find the probability the man will win. Should he play this game?
b)What is the probability of winning if he wins by getting atleast 4 heads in five flips ? Should he play this new game?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
5 heads:1%2A%280.7%29%5E5%2A%280.3%29%5E0=0.16807
4 heads:5%2A%280.7%29%5E4%2A%280.3%29%5E1=0.36015
3 heads:10%2A%280.7%29%5E3%2A%280.3%29%5E2=0.3087
2 heads:10%2A%280.7%29%5E2%2A%280.3%29%5E3=0.1323
1 heads:5%2A%280.7%29%5E1%2A%280.3%29%5E4=0.02835
0 heads:1%2A%280.7%29%5E0%2A%280.3%29%5E5=0.000243
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a)P=P%282%29%2BP%283%29%2BP%284%29%2BP%285%29=0.9692
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b)P=P%284%29%2BP%285%29=0.5282
It's not as good as before but still better than a fair coin which should be P=0.5.