Unit 8. Day 2.

CarnivalGame Groups of 2

CarnivalGame 1 2 3 4 Groups of 2

The spinner has four equal sections numbered 1–4 as shown below The spinner has four equal sections numbered 1–4 as shown below. To play the game, a student spins the spinner twice and adds the two numbers that the spinner lands on. If the sum is greater than or equal to 5, the student wins a prize. 1 2 3 4

Play the game 15 times. Complete the table. Turn 1st Spin 2nd Spin Sum 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 4 1 5 1 3 4 3 2 5 1 1 2 2 1 3 1 4 5 4 1 5 3 1 4 2 4 6 4 4 8 1 1 2 4 3 7 3 4 7 3 1 4 1 2 3

Some questions. Out of the 15 turns, how many times was the sum greater than or equal to 5? What sum occurred most often? What sum occurred least often? If students were to play a lot of games, what fraction of the games would they win? Explain your answer. Name a sum that would be impossible to get while playing the game. What event is certain to occur while playing the game?

Total number of observed occurrences of the event number of “favorable” outcomes P sum≥5 = Total number of observations number of possible outcomes P sum≥5 = 8 = 0.5 3 15 P 5 = 4 1 2 = 0.2 6 15 3 4

1 2 3 4 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 P sum≥5 = 8 = 0.5 3 0.5 3 15 𝑣𝑠 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 + 4 1 1 = 2 3 + 1 = 1 2 = 3 3 2 = 5 + + = 4 3 3 = 6 1 + 3 + 1 + 4 = 5 3 + 4 = 7 2 + 1 = 3 4 + 1 = 5 1 2 + = 3 4 + 2 2 2 = 6 2 + 3 = 5 4 + 3 = 7 2 + 4 = 6 4 + 4 = 8 3 4 P sum≥5 = 6 0.6 = 0.6 10

Example B: A student brought a very large jar of animal crackers to share with students in class. Rather than count and sort all the different types of crackers, the student randomly chose 𝟐𝟎 crackers and found the following counts for the different types of animal crackers. Estimate the probability of selecting a zebra. Animal Number Selected Lion 𝟐 Camel 𝟏 Monkey 𝟒 Elephant 𝟓 Zebra 𝟑 Penguin Tortoise   Total 𝟐𝟎 P 𝑧𝑒𝑏𝑟𝑎 = 3 = 0.15 20

2 1 10 = = 0.1 20 4 1 5 0.2 = = 20 4 = 20 = 20 1 5 Example C: P 𝑙𝑖𝑜𝑛 = Example D: P 𝑚𝑜𝑛𝑘𝑒𝑦 = = = 20 Animal Number Selected Lion 𝟐 Camel 𝟏 Monkey 𝟒 Elephant 𝟓 Zebra 𝟑 Penguin Tortoise   Total 𝟐𝟎 Example E: P 𝑝𝑒𝑛𝑔𝑢𝑖𝑛 𝑜𝑟 𝑐𝑎𝑚𝑒𝑙 = 4 1 5 = = 0.2 20 Example F: P 𝑟𝑎𝑏𝑏𝑖𝑡 = = 20

Some questions. Is there the same number of each kind of animal cracker in the jar? Explain your answer If the student randomly selected another 20 animal crackers, would the same results occur? Why or why not? Animal Number Selected Lion 𝟐 Camel 𝟏 Monkey 𝟒 Elephant 𝟓 Zebra 𝟑 Penguin Tortoise   Total 𝟐𝟎 If there are 𝟓𝟎𝟎 animal crackers in the jar, approximately how many elephants are in the jar? 5 𝑥 = 20 500 𝑡𝑜𝑡𝑎𝑙 𝑡𝑜𝑡𝑎𝑙 20𝑥 = 2500 20 20 𝑥 = 125