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| 8.2 Concepts A game involves rolling an ordinary six-sided die, and the number of dollars won on each toss is the number obtained on the die. If it costs $3 for each toss of the die, is this a fair game? Explain your reasoning. If it is not a fair game, how much should it cost for each toss of the die in order for this to be a fair game? Show how you arrived at your conclusion. 8.2 Teaching Students should also explore probability through experiments that have only a few outcomes, such as using game spinners with certain portions shaded and considering how likely it is that the spinner will land on a particular color. NCTM Standards 2000, page 181An elementary school teacher made two spinners, each with 10 equal parts and each part containing one of the digits from 0 through 9. The students were carrying out the activity of spinning first one spinner and then the other and adding the two digits. The students soon realized that the smallest sum of 0 and the largest sum of 18 did not occur very often. This lead to the question of which of the possible sums would occur most often. The teacher asked each student to make a prediction. Describe an activity the students could carry out to answer this question. Create and describe a game requiring sums of digits from these spinners. List some probability questions that could be answered from your activity and/or game. 8.2 Concepts Sometimes two events can each separately have a high probability of occurring, but the probability of both happening is less that 50%. Consider a sack with 7 red chips and 3 blue chips. What is the probability of randomly selecting two chips and getting both red? Describe two different methods of determining this probability. Create an example of three independent events that each have a fairly good chance of occurring, but the probability of all three occurring is less than 50%. Discuss the general notion that if several events with high probability are carried out, the probability of all occurring can be very small. |