In the game of blackjack as played in casinos in Las Vegas A

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 0.33. Find the probability that an average player wins

10 or more times in 26 hands.

Probability =

Solution

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    26      
p = the probability of a success =    0.33      
x = our critical value of successes =    10      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   9   ) =    0.656549344
          
Thus, the probability of at least   10   successes is  
          
P(at least   10   ) =    0.343450656 [ANSWER]