Suppose a slot machine has three independent wheels as shown in the figure below.**First Wheel:**- Orange- Cherry- Lemon- Bell- Plum- Orange- Bar- Plum- Cherry- Lemon- Orange- Bar- Lemon- Orange- Cherry- Lemon**Second Wheel:**- Cherry- Bar- Plum- Orange- Bell- Cherry- Plum- Bar- Orange- Cherry- Bell- Orange- Bar- Lemon- Bell- Cherry**Third Wheel:**- Cherry- Plum- Cherry- Plum- Cherry- Orange- Cherry- Bar- Orange- Bell- Cherry- Plum- Bar- Orange- Bell- CherryThe payoffs for the slot machine shown in the figure are in the following table.- First one cherry: 4 coins- First two cherries: 5 coins- First two wheels are cherries and the third wheel a bar: 11 coins- Three cherries: 11 coins- Three oranges: 13 coins- Three plums: 13 coins- Three bells: 20 coins- Three bars (jackpot): 55 coinsWhat is the mathematical expectation for playing the game with the coin being a quarter dollar? Assume the three wheels are independent. (Assume you are playing one coin. Round your answer to two decimal places.)\$______Please note: The goal is to calculate the expected value of playing this slot machine by considering each potential outcome's probability and multiplying it by its respective payoff, then summing all these values.

From the question we get , There are 20 figures in each wheel The probability of getting a figure x…

Answered: What is the mathematical expectation…

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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A lawyer considers taking a case figures that there is a 40% chance of winning the case in court and earning his firm $400,000, a 50% chance of losing the case in court and costing his firm $150,000, and a 10% chance of settling out of court and bringing in $200,000. What is the expected payoff of the case for the firm?
You are on a TV show. You have been asked to either play a dice game four times or accept a $50 bill. Thedice game works like this:If you roll a 1, 2, you lose $30. If you roll a 3, 4 or 5, you win $100. If you roll a 6, you lose $50.Should you play the game? Answer yes or no.__________ Use expected values and decision theory to justify your answer. Please round the answer to two decimal places.Expected value of four games is $__________.
Charlie buys a one-year term home insurance policy for $p, that will pay $200,000 in the event of a major catastrophe and $35,000 in the event of a minor catastrophe. Charlie's home has a 0.2% chance of a major catastrophe and a 0.7% of a minor catastrophe during the one year term. What did the insurance company charge Charlie for this policy if the company expected to break even?
A lawyer, considering taking a case figures that there is a two and five chances of winning the case in the court and earning his firm $400,000, a two and five chances of losing and costing his firm $250,000, and a one and five chances of settling out of court and bringing in $200,000. Should the lawyer take the case based on his expected payoff? explain using mathematical argument.
(QUEEN'S SECRET AND GENIES) In old days, there was a queen and she had a secret problem to solve. To get an answer to her secret problem, the queen bought one female and one male genie lamps. The probabilities that her secret problem can be solved by the male and female genies are 0.3 and 0.4 respectively. A Queen looking for divine help. Assume the queen keeps the genies independently away from each other with a fear that both could not harm her, what is the probability that the queen's secret problem is solved by at least one of the genies? Note: Please keep accuracy upto two decimal places.
Roulette: You bet on numbers 1-18. What's the likelihood of winning after one trial? Explain your answer.
If you were charged $8.00 to play this game, you would on average see a ..... (lose/gain) of ...... per spin.
B. Perimeter Shot - A perimeter shot, also known as a mid-range shot, is a jump shot or general field goal attempt that an offensive player can take inside of the three-point line and is worth 2 points. To practice this, Piel has to choose four different shooting spots among the five different spots in where he is comfortable of shooting. In previous games, his shot selection is 5% from the right baseline (Spot 1), 15% from the right elbow (Spot 2), 20% from the top of the key (Spot 3), 25% from the left elbow (Spot 4) and 35% from the left baseline (Spot 5). In this drill, a shooting spot can be selected once, multiple times, or not at all. This drill illustrates a random experiment with distribution. To help Piel decide, below is the partial table for the means and standard deviations of the random variable, Y, or the number of times he shoot the ball in a shooting spot. Shooting Spot E[Y] SD[Y] Spot 1 0.2 0.4359 Spot 2 0.6 0.7141 Spot 3 0.8 0.8000 Spot 4 the mean of 1.4 by will…
Answer the following question. In a recent competition, each of three teams played each other team once. The results are given in the table below. What was the score of the A vs. C game? Give A's goals first. Team A B C Wins 1 1 0 Losses Ties 0 1 0 1 2 0 Goals For Goals Against 6 3 2 4 2 5 (Remember: Your solution must show appropriate work or reasoning.)
Luis is playing a paint ball game. To win, he must capture the flag and choose the correct escape route. The chance that he captures the flag is 62%. The chance that he chooses the correct escape route is 68%. The probability that he does both is 41%. Create a Venn Diagram and determine the probability that: He captures the flag and chooses the correct route He only captures the flag He only chooses the correct route He doesn’t complete either task
Maria plays basketball and is a 64% free throw shooter (meaning on average she hits 64 of 100 free throws). Maria attempts five free throw shots in a typical game. During a 25-game season, Maria had a game in which she attempted five free throws and hit all five of them. Do you think she had a "hot" day, or was it just chance? Explain your reasoning. .……... Is the streak surprising? Explain. Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. The probability that she made five free throw tosses out of five is OB. The probability that she made five free throw tosses out of five is OC. The probability that she made five free throw tosses out of five is D. The probability that she made five free throw tosses out of five is which makes it very surprising. and the probability of it happening at least once in the season is which is very unlikely regardless of the number of games in the season. which is likely to…
Alyssa and Gabriel play a game. Alyssa rolls a die. If she rolls a 1, 2, or 3, Gabriel gives away $3. If Alyssa rolls a 4 or 5, he gives her $2. However if she rolls a 6, she gives him $22. Determine Alyssa's expectation and determine Gabriel's expectation

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