0. Rachel is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rachel tosses the dart once. She 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 the dart lands in slice 4. She loses $2.50 if the dart lands in slices 5, 6, 7, or 8. (a) Find the expected value of playing the game. dollars (b) What can Rachel expect in the long run, after playing the game many times? Rachel can expect to gain money. She can expect to win ( ) dollars per toss. Rachel can expect to lose money.

0. Rachel is playing a game of chance in which she tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random. This game is this: Rachel tosses the dart once. She 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 the dart lands in slice 4. She loses $2.50 if the dart lands in slices 5, 6, 7, or 8. (a) Find the expected value of playing the game. dollars (b) What can Rachel expect in the long run, after playing the game many times? Rachel can expect to gain money. She can expect to win ( ) dollars per toss. Rachel can expect to lose money.

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...

See similar textbooks

Similar questions

XYZ company has designed a new lottery scratch-off game. The player is instructed to scratch off one spot: A, B, or C. A can reveal "loser," "win $1," or "win $50." B can reveal "loser" or "take a second chance." C can reveal "loser," or "win $500." On the second chance, the player is instructed to scratch off D or E. D can reveal "loser" or "win $1." E can reveal "loser" or "win $10." The probabilities at A are 0.9, 0.09, and 0.01 respectively. The probabilities at B are 0.8 and 0.2. The probabilities at Care 0.999 and 0.001. The probabilities at D are 0.95 and 0.05. The probabilities at E are 0.5 and 0.5. Calculate the expected value of the game and provide recommendations to a decision-maker
A tennis game between two players consists of at most five games. The first player that winsthree games is the final winner. In how many ways can the game occur?
Español Kaitlin 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: Kaitlin spins the spinner once. She wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner stops on the number 3, and $7 if the spinner stops on the number 4. She loses $6.50 if the spinner stops on 5 or 6. (If necessary, consult a list of formulas.) 00 (a) Find the expected value of playing the game. | dollars (b) What can Kaitlin expect in the long run, after playing the game many times? O Kaitlin can expect to gain money. She can expect to win dollars per spin. O Kaitlin can expect to lose money. She can expect to lose dollars per spin. O Kaitlin can expect to break even (neither gain nor lose money). Save For Later Submit Assignment Check 2022 McGraw HilL LLC. AlLRiahts Reserved. Terms of Use Privacy Center Accessibility étv 8 MacBook Air DII F9 F10 F11 F7…
A game has a 10 dollar buy in. You have 20% to win nothing, 20% to win 5 dollars, 30% to break even, and 30% to win 20 dollars. What is the games EV? 画

Many casinos have a game called the Big Six Money Wheel, which has 54 slots in which are displayed a Joker, the casino logo, and various dollar amounts, as shown in the table at the top of the next column. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if the wheel stops on the same place as the player's bet, the player wins that amount for each dollar bet. Denomination Number of slots $40 (Joker) 1 $40 (Casino logo) 1 $20 2 $10 4 $5 7 $2 15 $1 24 If a player bets $4 on the $10 denomination, find the player's expectation. (Round your answer to two decimal places.)
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
In a lottery game, 4 numbers are chosen at random. Each number can take a value 1, 2, 3, or 4, and each value is equally likely. The numbers are chosen independently of each other. Use the method of equally likely outcomes to answer the following question: Which sequence of numbers is more likely to be drawn in the lottery, 1-1-1-1 or 4-2-3-1? Group of answer choices They are equally likely 1-1-1-1 is more likely 4-2-3-1 is more likely
Suppose you play a game with a biased coin. You play each game by tossing the coin once. and . If you toss a head, you pay $10. If you toss a tail, you win $11. if you play this game many times, will you come out ahead? (i.e. will you gain extra money from playing this game?) (Be sure to use fractions in the table.)
In a class there are 4 students who are 19 years old and obtained 80 pints in the midterm. There are 6 students who are 19 years old and obtained 50 pints in the midterm. There are 6 students who are 20 years old and obtained 80 pints in the midterm. There are n students who are 20 years old and obtained 50 pints in the midterm. There are no other students. We randomly pick a student in the class, let their age be X and their score by Y. If we are given that X, Y are independent random variables, then compute n.
A certain game involves tossing 3 fair coins, and it pays 13¢ for 3 heads, 6¢ for 2 heads, and 2¢ for 1 head. Is 6¢ a fair price to pay to play this game? That is, does the 6¢ cost to play make the game fair? The 6¢ cost to play is not a fair price to pay because the expected winnings are (Type an integer or a fraction. Simplify your answer.) c.
a game of chance played historically by Canadian Indians involved throwing eight flat beans into the air and seeing how they fell. The beans were symmetrical and were painted white on one side and black on the other. The bean thrower would win one point if either 0 or 8 white beans came up, and would lose one point for any other configurations. Does the bean thrower have the advantage in this game?