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What?? A Green Jawbreaker?
Place 10 jawbreakers in numbered brown lunch sacks. Use various combinations of two colors, 9-1, 8-2, 7-3, 6-4. To create an interesting situation, facilitate discussion and have some fun, place a single different colored jawbreaker in one bag so that the bag has three colors. Place the bags on a table in front of the class. Each group will be responsible for guessing the combination of colors that is in their bag. Have a student from each group come to the front, reach in the bag without looking, pull out a jaw breaker, show the rest of the group the color, write the color on the board, and put the jaw breaker back in the bag. Keeping the bags in front decreases the opportunity for students to peek inside the bag to see the colors. Discuss some of the properties of probability that are listed below. Have another person from the group come to the front, pick another jawbreaker and repeat the process. Ask if any group would like to guess the number combination of their sack? Give students an opportunity to discuss the contents of their sack. Have another student repeat the process. Allow group and whole class discussion of the samples taken this far. After each drawing take time to discuss some of the properties of probability. Continue to ask if they would like to draw one more time. I usually stop after 6 opportunities because this forces the students to make some decisions rather than doubling the numbers if you stop after five samples. Each group needs to come to a consensus regarding the contents of their sack and write their guess on the board. Those groups correctly guessing the contents of their bag will receive a jawbreaker. I then pick one group and ask them to explain their choice. At this time the teacher can try to convince the students to change their mind. Pick a sack, say, If I pull out a red jaw breaker would you change your mind? The teacher can ask for students with dissenting opinions from the consensus of the group to express their feelings. When finished reward all students with jawbreakers.
Below is a list of some properties of probability to discuss during the activity?
What is probability? Define probability.
Where is it used? Insurance, Disease/medical treatments, Genetics, Weather, Athletics, Gamble (responsibly), Doing or not doing homework, Retirement/investments
Notation for probability P(event)
P(event) = 0 means what?
P (event) = 1 means what?
Can P(event) ever be greater than one?
Probability of an event will always be between 0 and 1
If flipping coins yields four heads in a row, the probability of the next toss being a head is still one-half if the coin is balanced.
P(H) = .5 for coin toss, if a coin is flipped 100 times will you get exactly 50 heads and 50 tails? Why? Probability is based on a large number of trials. Anything can happen in the short run.
Everything must have an equal chance of occurring. You could not place nickels, dimes, and quarters in the sack because you could feel the difference in size. The sack could not be clear.
Stress that you dont know what is in the sacks and that each class events turn out different. Nothing is sure in probability.
How many would you draw out to have a good idea of the sack contents? To know for sure?
The sum of the probabilities of all possible events will equal one.
P(event) = A then P(not event) = 1-A This is called the compliment of an event.
EXTENSION ACTIVITY
Fill three sacks with jaw breakers, 8 red and 12 blue, 12 red and 8 blue, 3 red and 17 blue. Tell the students that you forgot which is which. Take one of the sacks and draw one at a time and replace. Repeat several times and have them decide which mixture has been chosen. Go to another sack and repeat the process. Go to the last sack and repeat. Allow them to change their guess and make sure that they justify their selections.
Is This Game Fair?
Number Cube Differences
The cost of playing this game is $1.00. Two number cubes are rolled. The absolute value of the difference between the numbers shown on the cubes is calculated. If the difference is a 0, 1 or 2 the player earns nothing. If the difference is a 3, 4 or 5 the player gets $2.00 .
Table of rolling of number cubes Table of differences of number cube
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12345611,11,21,31,41,51,622,12,22,32,42,52,633,13,23,33,43,53,644,14,24,34,44,54,655,15,25,35,45,55,666,16,26,36,46,56,6123456101234521012343210123432101254321016543210
Difference012345Probability of each event.
Must sum to 1 for all events6/3610/368/366/364/362/36Payment to player
000222Net amount to bank
Bank keeps amount bet.+1+1+1-1-1-1
Expected Value equals the sum of the probabilities of all events times the net value to the bank.
Expected value = P(Event1)*Net value (Event 1) + P(Event 2)*Net value(Event 2) + .
Expected value = EMBED Equation.3
Each time the game is played the bank earns 0.33 cents.
Challenge students to make the game fair, expected value of 0, by changing which numbers the bank and the player get or by changing the amount of money that is paid for differences.
Other possibilities with two die:
Sum of numbers
Sum of numbers even or odd
Product of numbers even or odd
Difference of numbers negative or positive
Doubles or not doubles
Flipping two or three coins
Lenny VerMaas page - PAGE 1
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