Can some one help me with this one I cant seem to figure itout There is a standa
ID: 2951397 • Letter: C
Question
Can some one help me with this one I cant seem to figure itout
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 are four of each 10 J Q K in a deck so theprobability is 4*4/52 = 4/13
b) The only information the "given" part tells me is that thedeck now has 51 cards and all 4 A's are still in play so theprobability should be 4/51.
c) This one is a conditional probability question: P[A|B] =P[AB]/P[B] The joint proability for A B is the probability of getting anycombination of A and a 10 J Q or K The total number of two card hands is: 52 choose 2 =52*51/2 The total number of hands that give a blackjack are: 4*4*4/2<----- This /2 is there to remove repeated combinations**
**The way I calculate number of hands for a certaincombination in this situations is breaking it up section bysection. For a two card had, the first section is card 1 which weneed to be a 10 J Q or K. There are 4 suits to a number so 4*4 isthe total ways for the first card. The second card is an A, this isgiven. So the total ways for the second card is 4*1. Therfore totalcombos for a blackjack hand is 4*4*4*1. In combinations withindistinct objects, you must remove repeated combinations, which isdone by dividing the total by n!
P[AB] = Total # of Blackjack Hands/ Total # of 2 cardhands = 4*4*4/52*51 =16/663 P[B] = P[Aces for the second card] = 4/51
P[A|B] = 16/663 / 4/51 = 16*51/4*663 = 4/13