In the game of blackjack as played in casinos in Las Vegas, Atlantic City, Niaga

Question

In the game of blackjack as played in casinos in Las Vegas, Atlantic City, Niagara Falls, as well as many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 0.36. Assume that each hand is independent and this probability stays constant. Find the probability that an average player wins

A. twice in 5 hands.

B. 10 or more times in 24 hands.

There are several books that teach blackjack players the "basic strategy" which increases the probability of winning any hand to 0.45. Assuming that the player plays the basic strategy, find the probability that he or she wins

C. twice in 5 hands

D. 10 or more times in 24 hands

Explanation / Answer

Binomial Problem with p = 0.36

A. twice in 5 hands.
P(x = 2) = 5C2*0.36^2*0.64^3 = binompdf(5,0.36,2) = 0.3397
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B. 10 or more times in 24 hands.
P(10<= x <=24) = 1 - P(0<= x <=9) = 1 - binomcdf(24,0.36,9) = 0.8373

2 ans) Binomial Problem with p = 0.45

A. twice in 5 hands.
P(x = 2) = 5C2*0.45^2*0.55^3 = binompdf(5,0.45,2) = 0.3369
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B. 10 or more times in 24 hands.
P(10<= x <=24) = 1 - P(0<= x <=9) = 1 - binomcdf(24,0.45,9) = 0.8383

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