24 According to the house statistician a casino estimates th

24. According to the house statistician, a casino estimates that it has a 51% chance of winning on any given hand of blackjack. The casino also assumes that blackjack hands are independent of one another. The casino randomly monitors its blackjack dealers, and as soon a dealer is found to lose 5 hands in a row, the casino stops the game at that dealer\'s table and checks the deck of cards that the dealer is using. The casino has just started monitoring a dealer. What is the chance that the game will be stopped at the table sometime within the next 8 hands of blackjack? A) .07 B) .09 C) .11 D) .13 E) .15

Solution

Let X is a random variable denoting lose of hands in a black jack

p =chance of loosing a hand = 49%

required to find loosing five hands in a row, and it can happen in 4 ways

Probability = 4 * 0.49^5 = 0.1129 =0.11

hence C is the correct choice