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- If P(AB)=0.7, is it possible that P(BA)=0.6? ExplainA family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?In three-card poker, a hand consists of three cards dealt from a deck of 52. How many different three-card poker hands are possible? (Order is not important.)
- Suppose that you want to get either four consecutive cards from the same suit or three cards with the same value. Your hand is shown here. You draw a card from the remaining 42 cards in the standard deck. Which probably is greater? Why? - drawing 5♥️, or - drawing 8♥️ or 8♠️The following are the rules of the game: One player is chosen to be the "It" that guards the preso (empty can). The rest of the players are the hitters, and each throws the pamato (slipper) to the toe-line to topple down the preso. If a player throws the farthest from the toe-line, he/she becomes the "It". The hitters are divided between the two opposite sides. When the hitters run out of throwing objects, the game translates into a chase. Players on one side will act as bait while those on the other side will try to kick the can to avoid being tagged. R2: R3: R4: R5: R6: Given the set of rules of the game, answer the following: 1. Identify the simple statements, compound statements, and the connectives involved in compound statements. Explain your answer. 2. Make a twist in the game by adding a new rule to the game or replacing one of the rules of the game.consider a game of 4×4 Tic-tac-toe in which a player must get four in a row to win. Determine the number of games that end on turn 7. Please dont give hand written solution
- Mario and Isabella are playing the Integer Card Game. The cards in their hands are shown: Mario's Hand 5,8, 8,-15 Isabella's Hand -4,5, 3, 2 8. -4 8. -15 3 What are the scores in each of their hands? Show your work. 2.A roulette wheel has 30 slots, consisting of 2 blues, 8 whites, and 20 red slots. You will receive P100 if the roulette stops spinning on a blue slot, you will receive P50 on a white slot, but you will be penalized P10 if the roulette stops spinning on a red slot. Let X be the amount you will recieve (or pay). What are the possible values of X? x= 2, 8, 20 x= 100, 50, -10 x= 100, 50, 10 x= 30, 2,8, 20Q2: According to a well-known legend, the game of chess was invented many centuries ago in northwestern India by a certain sage. When he took his invention to his king, the king liked the game so much that he offered the inventor any reward he wanted. The inventor asked for some grain to be obtained as follows: just a single grain of wheat was to be placed on the first square of the chessboard, two on the second, four on the third, eight on the fourth, and so on, until all 64 squares had been filled. If it took just 1 second to count each grain, how long would it take to count all the grain due to him?
- State if this scenario involves a permutation or a combination. Then find the number of possibilities. The student body of 10 students wants to elect a president, vice president, secretary, andtreasurer. A - Permutation; 5,040 B - Combination; 5,040 C - Permutation; 10! D - Combination; (10 - 4)!Mike and Bill play a card game with a standard deck of 52 cards. Mike selects a card from a well-shuffled deck andreceives A dollars from Bill if the card selected is a diamond and receives $1 from Bill if the card selected is an ace that is not adiamond. Otherwise, Mike pays Bill two dollars. Determine the value of A if the game is to be fair.Jane draws a marble from a box containing 5 red marbles, 3 green marbles, and4 blue marbles. She receives $2 for a red marble and $3 for a green marble that she draws.If she draws a blue marble, she loses $4. Is the game fair? How many dollars should Janepay for a draw in a fair game?