**Expected Value in a Dice Game**In this example, you are presented with a dice game where you win $100 if the die lands on the number 2, and you lose $15 otherwise. We need to calculate the expected value and determine whether it is advisable to play the game.**Game Description:**- Win $100 if the die lands on the number 2.- Lose $15 if the die lands on any other number (1, 3, 4, 5, or 6).**Question:**What is the expected value of this game?Should you play the game based on the expected value?**Options:**1. 4.17, yes2. -4.17, no3. 16.67, yes4. -16.67, no**Explanation:**To find the expected value, we use the following calculation:\[ \text{Expected Value (EV)} = (P(\text{win}) \times \text{win amount}) + (P(\text{loss}) \times \text{loss amount}) \]The probability $ P(\text{win}) $ of rolling a 2 on a fair six-sided die is $ \frac{1}{6} $.The probability $ P(\text{loss}) $ of rolling any other number (1, 3, 4, 5, or 6) is $ \frac{5}{6} $.Thus, the expected value calculation is:\[ \text{EV} = \left( \frac{1}{6} \times 100 \right) + \left( \frac{5}{6} \times -15 \right) \]\[ \text{EV} = \left( \frac{1}{6} \times 100 \right) + \left( \frac{5}{6} \times -15 \right) \]\[ \text{EV} = \left( \frac{100}{6} \right) + \left( \frac{-75}{6} \right) \]\[ \text{EV} = \frac{100 - 75}{6} \]\[ \text{EV} = \frac{25}{6} \]\[ \text{EV} \approx 4.17 \]Therefore, the expected value is positive (approximately $4.17),

Answered: a die lands on the number 2, you win…

a die lands on the number 2, you win $100. Otherwise, you lose $15. hat is he expected value? hould you play the game? = 4.17, yes -4.17, no 16.67, yes -16.67, no

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.FOM: Focus On Modeling: The Monte Carlo Method

Problem 3P: Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if...

See similar textbooks

Similar questions

You toss two six-sided dice. What is the probability that the total of the two dice is 5?
Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an 8,000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning and that of B winning if the game were to continue? The French Mathematician Pascal and Fermat corresponded about this problem, and both came to the same correct calculations though by very different reasonings. Their friend Roberval disagreed with both of them. He argued that player A has probability 34 of winning, because the game can end in the four ways H, TH, TTH, TTT and in three of these, A wins. Robervals reasoning was wrong. a Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform the experiment 80 or more times, and estimate the probability that player A wins. bCalculate the probability that player A wins. Compare with your estimate from part a.
Snake Eyes What ¡s the probability of rolling snake eyes ("double ones") three times in a row?
Medicine Out of a group of 9 patients treated with a new drug, 4 suffered a relapse. Find the probability that 3 patients of this group, chosen at random, will remain disease-free.
Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an $8000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning (and that of B winning) if the game were to continue? The French mathematicians Pascal and Fermat corresponded about this problem, and both came to the same correct conclusion (though by very different reasoning's). Their friend Roberval disagreed with both of them. He argued that player A has probability of Winning, because the game can end in the four ways H, TH, TTH, TTT, and in three of these, A wins. Roberval’s reasoning was wrong. Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform this experiment 80 or more times, and estimate the probability that player A wins. Calculate the probability that player A wins. Compare with your estimate from part (a).
In Example 8, what is the probability that an employee chosen at random has 30 or more years of service?