PROBABILITY WORKSHEET BlackJack Assume you are playing with a single standard de

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PROBABILITY WORKSHEET BlackJack Assume you are playing with a single standard deck of 52 cards. What is the probability of being dealt Blackjack (exactly 21 in 2 cards)? To get exactly 21, you need one Ace and you need either a 10, Jack, Queen, or King. In this game, you will play in pairs with a single deck of cards (face cards removed). Aces count as ones and all numbered cards count at face value. Players take turns flipping over two cards and finding the product. Regardless of who flipped the cards, Player 1 always gets one point if the product is even, and Player 2 always gets one point if the product is odd. Continue playing until one player reaches 20 points. Would you rather be Player l or Player 2? Do you think this is a fair game? ?fyou think it is not how could you alter the rules to make it fair? Race to the Top In this game, you are simulating a horse race by rolling a pair of standard six-sided dice. The bib numbers of the jockeys are the elements of the set (2,3, 4, 5, 6, 7, 8, 9, 10, 11, 12) to correspond to all possible outcomes for the sum of the two faces showing on the dice. Every time the dice are rolled, the horse with the corresponding bib number advances one space on the game board. Play continues until there is a winner (i.e. the first horse to advance 10 spaces). If you were betting on this race, which horse would you choose? Why? SRA Items Which of the following sequences is MOST likely to result from flipping a fair coin 5 times? HHHTTTHHTHTHTTT HTHTH All four are equally likely Select one or more explanations for the answer you gave in #2. Since the coin is fair, you ought to get roughly equal numbers of head and tails Since coin flipping is random, the coin ought to alternate frequently between landing heads and tails Any of the sequences could occur If you repeatedly flipped a coin five times, each of these sequences would occur about as often as any other sequence If you get a couple heads in a row, the probability of a tails on the next flip increases Every sequence of five flips has exactly the same probability of occurring a. b. e. d. e. f. Which ofthe con sequences in 2 is LEAST likely to result?

Explanation / Answer

Answer (1) BLACKJACK

Probability of selecting an Ace is (favorable outcome)/(total outcome)

favorable outcome = 4 because we have 4 different aces and total outcome = 52 because there are 52 cards in total

so, the probability of getting an Ace is 4/52

Now, we are remaining with only 51 cards because we have selected one Ace out of 52 cards with a probability of 4/52

now, total outcome = 51

we know that we have 4 cards of each 10's face, Queen, king and Jack, so a total of 4+4+4+4 = 16 cards

so, favorable outcome is 16 and total outcome is 16 for the second card

(we have already calculated the probability for first card using one ace which is 4/52)

So, probability of getting Ace and then either 10, jack, queen or king = (4/52)*(16/51)

And probability of getting either 10, jack, queen or king and then one ace = (16/51)*(4/52)

Adding both the probabilties to get the final answer, we get

(4/52)*(16/51) + (16/51)*(4/52) = 2*(16/51)*(4/52) = 2*(16/663) or 32/663

we can write 62/663 as 0.0483

So, Required probability is 0.0483 or 32/663

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