**Problem:**A simple carnival game involves flipping a coin to win money. If the coin lands on heads, the player loses $1 to the carnival. If the coin lands on tails, the player wins $2 from the carnival. Unbeknownst to the players, the coin is weighted so that it lands on heads 70% of the time. If this game is played 100 times, how much money does the carnival expect to win or lose?**Options:**A. Lose 10 cents B. Lose 10 dollars C. Lose 100 dollars D. Win 10 cents**Solution:**To determine the expected winnings or losses for the carnival, we need to calculate the expected value of a single game and multiply it by the number of games (100).1. **Probability and Payouts:** - Probability of Heads (P(H)): 0.70 - Probability of Tails (P(T)): 0.30 - Winnings for Heads (W(H)): -$1 (since the player loses $1) - Winnings for Tails (W(T)): $2 (since the player wins $2)2. **Expected Value (E) Calculation for a Single Game:** E = [P(H) * W(H)] + [P(T) * W(T)] E = [0.70 * (-1)] + [0.30 * 2] E = -0.70 + 0.60 E = -0.10 So, the carnival expects to win -$0.10 per game.3. **Total Expected Value over 100 Games:** Total E = 100 * E per game Total E = 100 * (-0.10) Total E = -10Therefore, the carnival expects to lose $10 over 100 games.So, the correct answer is:**B. Lose 10 dollars**

Given that the probability of getting head= 70%=0.70 So the probability of getting tail=1-0.70=0.30…

3. A simple carnival game involves flipping a coin to win money. If the coin lands on heads, the player loses S1 to the carnival. If the coin lands on tails, the player wins $2 from the carnival. Unbeknownst to the players, the coin is weighted so that it lands on heads 70% of the time. If this game is played 100 times, how much money does the carnival expect to win or lose? A. Lose 10 cents B. Lose 10 dollars C. Lose 100 dollars D. Win 10 cents

3. A simple carnival game involves flipping a coin to win money. If the coin lands on heads, the player loses S1 to the carnival. If the coin lands on tails, the player wins $2 from the carnival. Unbeknownst to the players, the coin is weighted so that it lands on heads 70% of the time. If this game is played 100 times, how much money does the carnival expect to win or lose? A. Lose 10 cents B. Lose 10 dollars C. Lose 100 dollars D. Win 10 cents

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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