4. Everyone has the same chance as Richard to win. If 160 people each play the game once, how many large stuffed animals will be won? Explain your reasoning. 5. If 160 people each play the game once, how many small stuffed animals will be won? Explain your reasoning. 6. If 160 people each play the game once, how many bat-shaped pencils will be won? Explain your reasoning. 7. If a large stuffed animal costs the game organizers $6, a small stuffed animal costs $1, and a pencil costs $0.25, how much profit do you expect the group to make from the 160 players? Advanced Mathematical Decision Making (2010) Charles A. Dana Center at The University of Texas at Austin Activity Sheet 9, 3 pages 23Student: Date: Probability: Expected Value Binomial Probability and Expected Value At the National Baseball Batting Contest, the organizers have set up game booths for the contestants. Richard wants to win a large stuffed animal. The rules of the game are as follows: You are pitched 5 fastballs, and you must hit them into a fair zone to count. If you successfully hit all 5 pitches, you win a large stuffed animal. If you successfully hit 3 or 4 pitches, you win a small stuffed animal. If you successfully hit 1 or 2 pitches, you win a bat-shaped pencil. If you miss all the pitches, you do not win a prize. The game costs $3 to play (each set of 5 fastballs). 1. What are the possible outcomes that Richard can have on his 5 swings? Explain or show how you arrived at your answer? 2. What is the probability of Richard successfully hitting the following? Justify your answers. a. All 5 pitches? b. 4 pitches? c. 3 pitches? d. 2 pitches? e. 1 pitch? f. 0 pitches? 3. Suppose Richard tries the game 10 times. How many times do you expect him to successfully hit the given amounts of times below? Justify your answers. a. 5 b. 4 c. 3 d. 2 e. 1 f. 0 Charles A. Dana Center at The University of Texas at Austin Advanced Mathematical Decision Making (2010) Activity Sheet 9, 3 pages 22