How do I solve this problem? There is a standard deck of 52 cards with which you

Question

How do I solve this problem?

There is a standard deck of 52 cards with which you will play agame of blackjack with the card dealer. (Of course, the deckhas been shuffled.) You will get a black jack if the value of yourcards sums to 21, with an “Ace” having a value of 11and the so-called face cards having a value of 10. (Those ofyou who know how to play black jack know that an “Ace”can also have a value of 1. To make this simpler, let’sjust let an “Ace” equal 11.) Two cards are dealtto you and two cards to the dealer. You are trying to win thegame.

a)     The dealer offer you two ways he could deal the cards toyou.

·         Method1: He deals you a card, then he takes a card; he deals you asecond card and then deals himself a second card.

·         Method2: He deals you two cards then he deals himself two cards.

·        

Under which method are you more likely to get a “blackjack” with just the first two cards dealt you?

b)     What is the probability the first card will be an ace?

c)       Given the first card was anace, what is the probability the second card is a 10, Jack, Queenor King?

Explanation / Answer

a) Method 2 gives you a better chance of getting a blackjack. Youdon't need any calculation to see this. In Method 1 thedealer takes a card before you can get your second card. If supposeyou got an ace for the first card the dealer may end up taking oneof the 16 suit cards you need to get a blackjack. This possibilityreduces the probability of you getting a blackjack. Ifinstead you draw two cards and then he draws two cards you've got abetter chance since the dealer doesn't have the opportunity to takethe cards you need. b) There are 4 aces and 52 cards so the probability is 4/52 =.0769 c) If the first card is an ace then there are 51 cards left. The are 16 cards that are either 10, Jack, Queen, or King sincethere are 4 of each and 4*4 is 16. Thus the probability is just16/51 = .3137

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