You have a bag with 3 red balls and 2 blue balls. You choose 3 balls at random from the bag without replacement. (Same as in #4.) We play a game: You pay $5 to play, and I will pay you $10 for every blue ball you get. Let Y be how much money you make. a. What is the expected amount of money you make each game?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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**Problem 9: Analyzing Expected Earnings in a Ball Selection Game**

You have a bag containing 3 red balls and 2 blue balls. You will randomly choose 3 balls from the bag without replacement. This scenario is the same as in problem #4. In this game, you pay $5 to participate. For each blue ball you draw, you earn $10. Define the variable \( Y \) as the amount of money you make.

a. Calculate the expected amount of money you earn for each game.
Transcribed Image Text:**Problem 9: Analyzing Expected Earnings in a Ball Selection Game** You have a bag containing 3 red balls and 2 blue balls. You will randomly choose 3 balls from the bag without replacement. This scenario is the same as in problem #4. In this game, you pay $5 to participate. For each blue ball you draw, you earn $10. Define the variable \( Y \) as the amount of money you make. a. Calculate the expected amount of money you earn for each game.
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