Question

Consider the casino game of Roulette where players place $1 bets on color (either red or...

Consider the casino game of Roulette where players place $1 bets on color (either red or black). The probability of winning a single bet is 18/38, slightly in the casino’s favor.

a. For 1000 such bets, the expected gain for the casino is $52.63, the standard deviation is $31.58, and the distribution of possible gains is approximately normal. Find the probability that the casino makes money overall after 1000 bets.

b. For 5000 such bets, the expected gain for the casino is $263.16, the standard deviation is $70.61, and the distribution of possible gains is approximately normal. Find the probability that the casino makes money overall after 5000 bets.

Math   Statistics-And-Probability   
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Answer #1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ= 52.63
std deviation   =σ= 31.580

probability that the casino makes money overall after 1000 bets:

probability =P(X>0)=P(Z>(0-52.63)/31.58)=P(Z>-1.67)=1-P(Z<-1.67)=1-0.0475=0.9525

b)

  probability that the casino makes money overall after 5000 bets:

probability =P(X>0)=P(Z>(0-263.16)/70.61)=P(Z>-3.73)=1-P(Z<-3.73)=1-0.0001=0.9999
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