Question

You play roulette 1000 times, betting $10 on red each time. What is the probability you come out ahead? Show that this Binomial probability model can be approximated by a Normal model. Then use this applicable Normal model to solve the problem.

Answer 1

P(Red) = 18/38

hence probability of win = p = 18/38

S =X1 + X2+ ...X1000

S follow binomial distribution with n = 1000 and p = 18/38

the probability you come out ahead = P(S > 500)

S can be approximated by normal distribution with mu = np and sd = sqrt(npq)

binomial approximation to normal
mean	473.6842
sd	15.789474

P(S > 500)

= P(S >= 500.5) continuity correction

= P(Z > (500.5 - 473.6842)/15.789474)

= P(Z > 1.6983 )

= 0.0447

Please rate if helpful