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Your dad is challenging you at baseball. He will throw 3 fastballs and you must hit them in a fair zone to count. Assume you have a 50/50 chance of hitting in the fair zone. If you hit all fastballs 3 in a fair zone, you will earn $30. If you hit 2 in a fair zone, you will earn $10. If you hit 1 in the fair zone, you don't get any money. Lastly, if you hit zero, you will owe your dad $15. What is the probability you will win $30? [ What is the probability you will earn $10? What is the probability you will earn $0? What is the probability of losing $15? What is your expected value?

Your dad is challenging you at baseball. He will throw 3 fastballs and you must hit them in a fair zone to count. Assume you have a 50/50 chance of hitting in the fair zone. If you hit all fastballs 3 in a fair zone, you will earn $30. If you hit 2 in a fair zone, you will earn $10. If you hit 1 in the fair zone, you don't get any money. Lastly, if you hit zero, you will owe your dad $15. What is the probability you will win $30? [ What is the probability you will earn $10? What is the probability you will earn $0? What is the probability of losing $15? What is your expected value?

A First Course in Probability (10th Edition)
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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**Question 10** Your dad is challenging you at baseball. He will throw 3 fastballs and you must hit them in a fair zone to count. Assume you have a 50/50 chance of hitting in the fair zone. - If you hit all 3 fastballs in a fair zone, you will earn $30. - If you hit 2 in a fair zone, you will earn $10. - If you hit 1 in the fair zone, you don't get any money. - Lastly, if you hit zero, you will **owe** your dad $15. **Questions:** 1. What is the probability you will win $30? (Input field here) 2. What is the probability you will earn $10? (Input field here) 3. What is the probability you will earn $0? (Input field here) 4. What is the probability of losing $15? (Input field here) 5. What is your expected value? (Input field here) **Explanation:** - The probability of hitting all 3 fastballs (HHH) in a fair zone (since each hit has a 50/50 chance): \( P(3 hits) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \) - The probability of hitting exactly 2 fastballs (HHM, HHK, HMH, KHH) in a fair zone: \( P(2 hits) = 3 \times \left(\frac{1}{2}\right)^3 = 3 \times \frac{1}{8} = \frac{3}{8} \) - The probability of hitting exactly 1 fastball (HMK, KMH, MHK) in a fair zone: \( P(1 hit) = 3 \times \left(\frac{1}{2}\right)^3 = 3 \times \frac{1}{8} = \frac{3}{8} \) - The probability of hitting zero fastballs (MMM) in a fair zone: \( P(0 hits) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \) **Expected Value Calculation:** - Expected value \( E \) = \( \sum (Probability \times Outcome) \) -
Transcribed Image Text:**Question 10** Your dad is challenging you at baseball. He will throw 3 fastballs and you must hit them in a fair zone to count. Assume you have a 50/50 chance of hitting in the fair zone. - If you hit all 3 fastballs in a fair zone, you will earn $30. - If you hit 2 in a fair zone, you will earn $10. - If you hit 1 in the fair zone, you don't get any money. - Lastly, if you hit zero, you will **owe** your dad $15. **Questions:** 1. What is the probability you will win $30? (Input field here) 2. What is the probability you will earn $10? (Input field here) 3. What is the probability you will earn $0? (Input field here) 4. What is the probability of losing $15? (Input field here) 5. What is your expected value? (Input field here) **Explanation:** - The probability of hitting all 3 fastballs (HHH) in a fair zone (since each hit has a 50/50 chance): \( P(3 hits) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \) - The probability of hitting exactly 2 fastballs (HHM, HHK, HMH, KHH) in a fair zone: \( P(2 hits) = 3 \times \left(\frac{1}{2}\right)^3 = 3 \times \frac{1}{8} = \frac{3}{8} \) - The probability of hitting exactly 1 fastball (HMK, KMH, MHK) in a fair zone: \( P(1 hit) = 3 \times \left(\frac{1}{2}\right)^3 = 3 \times \frac{1}{8} = \frac{3}{8} \) - The probability of hitting zero fastballs (MMM) in a fair zone: \( P(0 hits) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \) **Expected Value Calculation:** - Expected value \( E \) = \( \sum (Probability \times Outcome) \) -
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