e fair?
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- After giving the lotto a try you decide to go back to Clayton Campus for some more gambling action. Theyare playing a die tossing game where you win a brand new home if you roll all sides of the die within 7rolls. Your crystal ball can see into the future and tells you that when you roll the die 7 times you don't seethe same number appear twice in a row. You decide to bet your entire rent for the year and try to win thehouse. You toss a fair six-sided die 7 times. Consider the following events, A = “each value appears atleast once” and B = “the outcome is alternate in numbers (i.e., a specific face of the die cannot be observed to occur directly after it was observed on the previous roll but it may have occurred elsewhere inthe sequence of rolls)”. What is p(A|B)? Are you likely to win the house?You draw a card from a deck of 52 cards. If the card is a spade, you win $5, but if the card is not a spade you lose $2.What is your expected earning from this game?Your friend offers to place a bet with you. He will pay you $2 if your favorite sports team wins the game on Tuesday night. But you will pay him $3 if his team wins. Your team has an 55% chance of winning, whereas his only has a 45% chance. This bet is in your favor. True or False?
- Your friend throws two dice and tells you that one of the dice is a 4. What is the probability that the sum of the dice is 8 or more?You play a game with two-six sided dice. If you roll a sum of 4 or 7, you win P400 If you roll a sum of 10, you win P200. However, you lose P300 for anything else. If you continue to play the game, how much do you expect to win or lose in the game?There is a game of chance called "Lightning Dice" at a charity carnival. It costs $2 to play. The player then rolls 4 dice. If the player rolls 3 or more sixes, then the player wins $30. Otherwise, the player wins nothing. How much can you expect to gain or lose if you play this game 68 times?
- a pair of dice is rolled once. Suppose that you lose 9$ if the dice sum to 5 and win 10$ if the dice sum to 11 or 8. How much should you win or lose if any other number turns up in order for the game to be fair?A and B play the following game. They throw alternatively a pair of dice. Whosoever gets sum of the two numbers on the top as seven wins the game and the game stops. Suppose A starts the game. Find the probability (a) A wins the game (b) B wins the game.Suppose that you repeatedly roll a pair of fair dice and keep track of the sum. What is the probability that you see a sum of 7 before you see an even sum 3 times? (In particular, you keep track of how many evens you roll, and you want the probability that you roll a 7 before you get to 3 evens.
- If a pair of dice is tossed, find the probability of getting a total of 6 or a 12?A game is player with a pair of tetrahedral ( four sided) dice. Each die has four faces numbered 1,2,3,and 4. To play, roll the two dice and record the sum of the values on the down faves. What is the probability of rolling a sum of 7A teacher is making a student list for her field trip. She has decided to select a total of 10 students. She has 9 boys and 11 girls. What is the probability that 5 of the selected guests are boys? Show steps and solution.
