70. A has six shares in the lottery in which there are three prizes and ten blanks. B has two shares in a lottery in which there are four prizes and eight blanks. Which has the better chance to win a prize ?
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- At the National Baseball Batting Contest, the organizers have set up game booths for the contestants. Richard wants to win a large stuffed animal. The rules of the game are as follows: You are pitched 5 fastballs, and you must hit them into a fair zone to count. • If you successfully hit all 5 pitches, you win a large stuffed animal. If you successfully hit 3 or 4 pitches, you win a small stuffed animal. • If you successfully hit 1 or 2 pitches, you win a bat-shaped pencil. If you miss all the pitches, you do not win a prize. • The game costs $3 to play (each set of 5 fastballs). Everyone has the same chance as Richard to win. If 160 people each play the game once, how many large stuffed animals will be won?To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $6 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting th color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $7. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. P(X) Enter a fraction, integer, or exact decimal. Do not approximate (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. (c) Is this game fair? O Yes O NoGreen Red Orange Purple Yellow 3. Caitlyn and Tabitha want to fairly decide who will take the family dog on a walk, so they roll a fair six-sided die and spin the spinner above. Caitlyn will walk the dog if the die roll is a 1, 2, or 3 and the spinner lands on orange or green. Tabitha will walk the dog if the die roll is a 4 or 6 and the spinner lands on red, yellow, or purple. They will continue the experiment until one of the events occurs. Does the experiment provide a fair way to decide who walks the dog? Explain using probability.
- 4. Find the counting problem below: a. 4x5x6x...x1000 b. (50 10) c. (255) d. 25 5 e. 50 1014 16 18 a) How many times were the sum of the three dice more than 14? b) What proportion of the time was the sum of the three dice more than 14? c) How many times were the sum of the three dice at most 7? d) What proportion of the time was the sum of the three dice at most 7? Question Help: D Post to forum 00000 0000 00000000000 000000002 0000000000000 0000000f 000000 00000ot 00 0000000 0000to 0000 OF 006. You and your friend decide to play a game at a carnival that costs you $1 to play. The game involves flipping two coins and rolling a 6-sided die. If you flip two heads and roll a 3 on the die you win $25. If you flip two heads and roll an even number, you win $10. If you flip two tails with any dice roll, you win $5. а. List all of the possible outcomes for this game (i.e., the sample space). b. Calculate your expected value for this game. Game Outcome Probability c. Is this game profitable over time? How do you know?
- A fair did is rolled two times. What is the probs that both rolls are 3?5. Divide and conquer. You're again facing your friend, Brenda, in a "candy-off” game involving a pile of 100 caramels and the winner's prize: one peppermint patty. (Like before, you still LOVE peppermint patties!). On their turn, each player can remove aSuppose that you and a friend are playing cards and decide to make a bet. If your friend draws three twos in succession from a standard deck of 52 cards without replacement, you give him $100. Otherwise, he pays you $10. If the same bet was made 25 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary. Answer Кeypad Keyboard Shortcuts O Win O Lose %24
- An experiment is pulling a ball from an urn that contains 12 blue balls and 10 red balls.A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.
