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. An opening hand in the game Blackjack is made up of two cards with the following point values:• Aces are worth 11 points.• Jacks, Queens, and Kings are worth 10 points each.• All other cards are worth their number (ie a 4 is worth 4 points, a 7 is worth 7 points, etc.)Greatly oversimplifying things, the goal of the game is to get exactly 21 points. In the questionsbelow, assume that an opening hand is drawn from a freshly shuffled deck, and that cards are putback and then reshuffled in between trials. (Note: this is not how blackjack actually works.) Forthis question, show all of your work.(A) What is the expected value of an opening hand of blackjack?(B) What is the variance of an opening hand of blackjack?(C) What is the probability of getting exactly 21 in an opening hand?(D) If you know that the first card you draw is an ace, what is the probability of getting exactly21 in an opening hand? |
Answer» Probability of getting exactly 21 in an opening hand = 0.048Step-by-step explanation: Ace = 11 JACK , Queen , KINGS , & card 10 = 10 To get 21 we need to get Ace + either of Jack , Queen , kings , & card 10 Ace = 4 either of Jack , Queen , kings , & card 10 = 4 * 4 = 16 probability of getting exactly 21 in an opening hand = (4/52)(16/51) + (16/52)(4/51) = 2 * 64 / (52 * 51) = 64/ (26 * 51) = 32/(13 * 51) = 32/663 = 0.048 if first card you drawn is an ace then probability of getting exactly 21 in an opening hand = 16/51 = 0.314 Learn more: Find the probability distribution of the numbers obtained in THROWING ... A SAMPLE of four chocolate bars are randomly selected from a box of ... The probability distribution of a discrete r.v. X is GIVEN in table (i ... |
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