I need some help with this one, can some one show me how tosolve this problem Th
ID: 2951407 • Letter: I
Question
I need some help with this one, can some one show me how tosolve 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) What is the probability the first card will be a 10, Jack, Queen orKing?
b) Given that the first card was a 10, Jack, Queen or King, what isthe probability the second card is an ace?
c) When the dealer deals youthe two cards first, the FIRST card is dealt face down, so youcan’t see its value. The second card is face up so youcan see it. Given that the second card (the pone youcan see) is an ace, what’s the probability you made ablackjack? (That is, what is the probability the firstcard is an ace, 10, Jack, Queen, or King.
NOTE: It is NOT the probability you found in part b. Inpart b, the second card had not been drawn yet. Now that ithas, and it was an ace, that has changed the remainingpossibilities.
Explanation / Answer
a) There 4 of each suit and 4 suits we are interested in, so thereare 4*4 = 16 cards that are either 10, Jack, Queen, King There are 52 cards total. So the probability is 16/52 =.3077 b) So now there is one less card in the deck giving a total of 51cards. There are 4 aces so the probability of getting an ace is4/51 = .0784 c) So the face down card can have 51 possible identities now thatwe know the value of the face up card. We want to know theprobability that the face down card is a 10, Jack, Queen, orKing. From part a we know there are 16 types of these cardsso the probability that the face down card is one of those is just16/51 = .3137. (note the question says another ace would make a blackjack but thisis incorrect since the question says an ace has a value of 11 andif the first card is also an ace, that would give a point value of22. If you wanted to include the probability of getting an aceyou'd just add 3 to the numerator to get 19/51)