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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

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 (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**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, yes 2. -4.17, no 3. 16.67, yes 4. -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),
Transcribed Image Text:**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, yes 2. -4.17, no 3. 16.67, yes 4. -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),
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