Answer:
Step-by-step explanation:
Given that 10000 times a fair coin is flipped. Since fair coin prob for head of tail =0.5
If tail comes it will be taken as 1. Hence for the sum to be less than 5000, no of heads <5000
Since trials are large we approximate to normal with mean = np = 5000 and variance = np(1-p) = 2500
Thus no of heads x is normal with (5000, 50)
[tex]P(X<5000) = P(x<5000.5)\\= P(Z<\frac{0.5}{50} )\\=0.5-0.0040\\=0.4960[/tex]
Since this prob is less than 0.5 only minimum amount to be bet i.e. 1 dollar
If sum of coins <5100, then Z = [tex]\frac{5100-5000}{50} =2[/tex]
P(Z<2) = 0.9500
This time we can bet maximum of 100 dollars as probability is very high nearer to 1.
