Investigation 5 - Binomial Outcomes - Applications - Page 105 - CMP#3 - Grade 7
1. It costs six tickets to play the Toss-a-Penny game at the school carnival. For each turn, a player tosses a penny three times. If the penny lands heads up two or more times in a turn, the player wins ten tickets to spend on food and games.
a. Suppose Benito plays the game 80 times. How many tickets can he expect to win?
Possible outcomes as he tosses a penny three times:
HHH
HHT
HTH
HTT
THH
THT
TTT
TTH
He may win in 4 of the 8 outcomes. There is a 50% probability that he will win.
As he plays 80 times, it is expected that he will win 40 times. He expects to win 40*10 tickets = 400 tickets in 80 turns.
b. What's is the average number of tickets Benito can expect to win or to lose per turn?
In 80 turns, he has to pay 6 tickets times 80 = 480 tickets. Overall, in order to win 400 tickets, he will lose 480 tickets. The average loss will be 80 / 80 = 1 ticket per turn.
09/20/2021
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