Moss, Laura Willis South Shore Community Academy

Objectives: The students will derive a general formula for the probability of a given event given each possible outcome is equally likely. Apparatus Needed: 6 dice 30 colored balls (1 each of five different colors) 6 coins 6 paper plate holders 6 plastic cups 6 paper bags 19 ping pong balls (numbered from 0 to 18) Recommended strategy: The students were told they had an opportunity to win a prize in today's class by playing the lottery. They were to pick a 3 digit number, a 4 digit number (repeats are allowed) and a combination of 4 numbers from 1 to 18 (no number could be chosen twice). The students were divided into groups of 3 or 4. Each group received a paper bag containing 1 die, 5 colored balls (1 of each color-blue, green, yellow, orange and pink), 1 coin, 1 paper plate holder and 1 plastic cup. Each group had to conduct three experiments. 1. Flip the coin 50 times into the paper plate holder, record the results (heads or tails). 2. Pull a ball from the bag, record its color, replace the ball and repeat this process a total of 50 times. 3. Use the cup to shake the die. Roll the die into the paper plate holder. Record the result and repeat the process 60 times. As a class the data from each experiment was collected. The students were asked questions such as: Were the results of each experiment what you would have expected? What would you expect if we were to repeat the process 1000 times? 10,000 times? 10,000,000 times? The class then generated the formula for the probability of an event P(E) P(E) = number of favorable outcomes number of possible outcomes Then the class discussed whether or not the formula will tell us exactly what will happen for a given event. More examples were discussed. The "lottery" ended the lesson. Students with a knowledge of permutations and combinations can calculate the probability of each event. 1 1 P(3 digit number) = --- = ---- 103 1000

1 1
P(4 digit number) = --- = ------
104 10,000

P(4 number from 1 to 18) = 1 = 1
18! 3060

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