Michael is playing a game of chance in which he tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on anumbered slice at random.This game is this: Michael tosses the dart once. He wins $1 if the dart lands in slice 1, $2 if the dart lands in slice 2, $5 if the dart lands in slice 3, and $8 if thedart lands in slice 4. He loses $6.50 if the dart lands in slices 5, 6, 7, or 8.(a) Find the expected value of playing the game.| dollars(b) What can Michael expect in the long run, after playing the game many times?O Michael can expect to gain money.He can expect to win dollars per toss.O Michael can expect to lose money.He can expect to lose|dollars per toss.O Michael can expect to break even (neither gain nor lose money).

a) There is total 8 equal-sized slices in the dartboard, which are numbered from 1 to 8.

Answered: Michael is playing a game of chance in…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Lisa is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random. This game is this: Lisa spins the spinner once. She wins $1 if the spinner stops on the number 1, $4 if the spinner stops on the number 2, $7 if the spinner stops on the number 3, and $10 if the spinner stops on the number 4. She loses $11 if the spinner stops on 5 or 6. (a) Find the expected value of playing the game. | dollars (b) What can Lisa expect in the long run, after playing the game many times? O Lisa can expect to gain money. She can expect to win dollars per spin. O Lisa can expect to lose money. She can expect to lose dollars per spin. O Lisa can expect to break even (neither gain nor lose money).
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Ravi is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized slices, as shown below. The wheel has 2 black slices, 4 grey slices, and 4 white slices. When the wheel is spun, the arrow stops on a slice at random. If the arrow stops on the border of two slices, the wheel is spun again. (a) If the arrow stops on a grey slice, then Ravi wins a gift card. Find the odds against Ravi winning a gift card. 0 (b) If the arrow stops on a grey slice, then Ravi wins a gift card. Find the odds in favor of Ravi winning a gift card. X to
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A game involves drawing a single card from a standard deck. The player receives $10 for an ace, $5 for a king, and $1 for a red card that is neither an ace nor a king. Otherwise, the player receives nothing. If the cost of each draw is $2, should you play? Explain your answer mathematically.
You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $⁢4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $⁢5 if the spinner lands on blue and $⁢15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?
At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1–4), noting the number showing. If the die shows a 3 and the coin shows tails, then you win $22. If the coin shows heads and the die shows an even number, then you win $9. 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. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent.

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