2) Describe a scenario involving pulling two consecutive cards from a deck that would be considered INDEPENDENT
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- We will draw randomly with replacement from a simplified 13 card deck with 4 face cards (A, J, Q, K), and 9 numbered cards (2, 3, 4, 5, 6, 7, 8, 9, 10). If we draw cards with replacement 13 times, and if the number of face cards is greater than or equal to 4, we lose. Otherwise, Jade loses. We play the game once and we lose, observing 8 total face cards. We are angry and accuse Jade of cheating! Jade is adamant, however, that the deck is fair. Jade's model claims that there is an equal chance of getting any of the cards (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), but we do not believe her. We believe that the deck is clearly rigged, with face cards (A, J, Q, K) being more likely than the numbered cards (2, 3, 4, 5, 6, 7, 8, 9, 10). Assign deck_model_probabilities to a two-item array containing the chance of drawing a face card as the first element, and the chance of drawing a numbered card as the second element under Jade's model. Since we're working with probabilities, make sure your…Suppose we have a deck of cards, but some of the cards are missing. That is, instead of 52 cards, we have 48 cards. My friend wants to play a magic trick - he wants me to pick a card, remember it, put it back in the deck, then shuffle the deck. He claims he can find that card. Clearly, my friend keeps track of my card somehow, but if he did not keep track, and the cards were perfectly randomized, what would be the probability that he would select my card from the deck? Round your answer to 4 decimal places. Recall Canvas truncates trailing Os automatically without loss of marks - that means if you enter something like 0.5000, Canvas changes it to 0.5, and you do not lose marks as a result.for part a) don't you need to consider the scenario in which each player wins with tails and the other 2 players get heads
- A standard deck of 52 cards consists of 4 suites (hearts, diamonds, spades and clubs) each containing 13 different values (Ace, 2, 3, …, 10, J, Q, K). If you draw some number of cards at random you might or might not have a pair (two cards with the same value) or three cards all of the same suit. However, if you draw enough cards, you will be guaranteed to have these. For each of the following, find the smallest number of cards you would need to draw to be guaranteed having the specified cards. Prove your answers. a. Three of a kind (for example, three 7's). b. A flush of five cards (for example, five hearts). c. Three cards that are either all the same suit or all different suits.A man just bought 6 suits, 11 shirts, and 15 ties. All of these suits, shirts, and ties coordinate with each other. If he is to randomly select one suit, one shirt, and one tie to wear on a certain day, how many different outcomes (selections) are possible?7. In a chess competition involving some men and women, every player needs to play exactly one game with every other player. It was found that in 45 games, both the players were women and in 190 games, both players were men. What is the number of game in which one person was a man and another person was a woman? * 12 40 180 200 8. In a locality, there are ten houses in a row. One night, a thief planned to steal from three houses in the locality. In how many ways can the thief plan such that no two houses are next to each other? * 56 73 80 120 9. In how many ways can you group 12 people into 2 groups of 3 people and 3 groups of 2 people? * 1, 663, 200 2, 796, 330 4, 862, 200 5, 681, 030 .
- A box contains 6 card labelled 1,2,3,4,6, and 8. A game consists of drawing two cards in succession at random and without replacement and writing the digits from left to right in the order drawn (for example, drawing 3 and then 8 would yield the number 38, while drawing 8 and then 3 would yield the number 83). If the number thus constructed is greater than 50, then the player wins $20. If the number thus constructed is less than 50 but even, the player wins $10. Otherwise, the player loses $20. What is a player's expected winnings on this game (in dollars)?a bag contains 8 blue chips, 5 red chips, and 4 white chips. if two chosen at a random, what is the probabilitiy they will both be white?In a survey of 1200 people, 80 indicated they were going to buy a new car, 70 said they were going to buy a new TV and 65 said they were going to buy a new stove. Of these, 30 were going to buy both a car and a TV, 35 were going to buy a car and a stove and 20 were going to buy a stove and a TV. Twenty people said they were going to buy all three items. A person is selected at random from this 1200 people . Given that this person was not going to buy a TV, what is the probability that he /she was not going to buy a car ?
- A product shipment contains 6 computer chips, of which two (2) are defective. If an inspector selects 4 chips at random for an order, without replacement, how many ways are there of picking both defective chips in this order (of 4 chips)? Order does not matter.“ You are dealt five cards from a standard deck of 52 cards. How many of these handshave at least one queenandat least one spade. ”He breaks this into two cases. In the first case, he looks at hands which contain the queen of spadesQ♠. There is 1 way of choosing the Queen of Spades, and51C4ways of choosing the other fourcards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queenspade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades sothat he doesn’t overlap case 1. This gives49C3ways of choosing the last three cards. He concludesthat the answer is51C4+ (3·12·49C3). His answer is incorrect. Explain why, and give the correctanswer.Consider a deck of 52 cards with 4 suits and 13 cards (2-10,J,K,Q,A) in each suit. Jack takes one such deck and arranges them in a line in a completely random order. Now he wants to find the number of "Power Trios" in this line of cards. A "Power Trio" is a set of 3 consecutive cards where all cards are either a Jack, Queen or King (J,Q or K). A "Perfect Power Trio" is a set of 3 consecutive cards with exactly 1 Jack, 1 Queen and 1 King (in any order). Find the expected number of Power Trios that Jack will find. Find the expected number of Perfect Power Trios that Jack will find.
