a) (Picture on the left) Spin a spinner with 2 equal sections. One red, and one blue. Then flip a coin. This is equally likely. There is a 25% chance for each outcome in this situation. The outcomes are: R, H / R, T / B, H / B, T.
b) First, spin a spinner with 2 equal sections. Half is white and the other half is black (50-50). Then, pull out a marble from a bag. There are 4 marbles in the bag. 2 are red and 2 are blue. There is a 25% chance for each outcome. Outcomes: W, R / W, B / B, R / B, B.
c) It is a 1-1 situation free throw. This means that you can shoot again only if you made the first shot. If you didn't make the first shot, you are unable to shoot a second time. The player has a 50% shooting average. They have a 25% chance of scoring 2 points (making both shots), and a 25% chance of scoring one point. So, the player has a 50% chance of scoring 0 points, or not making any shots at all.
d) First roll a dice and pick a block from a bag. The dice is 6 sided, with the sides equally divided. There are 2 blocks in the bag. One yellow, and one blue. The outcomes are: 1, Y / 1, B / 2, Y / 2, B / 3, Y / 3, B / 4, Y / 4, B / 5, Y / 5, B / 6, Y / 6, B.
2. You can use an area model or a simulation to determine the probability of a situation that involves two actions. Explain how each of these is used.
~ An area model is used to find the theoretical probability of a situation that involves two actions. Going back to situation c, I used an area model to show the percent chance of scoring 0 points, 1 point, and 2 points. A simulation is used to find the experimental probability of a situation. In a simulation, an experiment is conducted, therefore finding the experimental probability. For example, with situation c, I could do a simulation where the player shoots baskets a certain number of times. The more trials, the more accurate the data will be. I would record the data from each time he attempted to shoot.
3. Describe how you would calculate the expected value for a probability situation.
~ One way is to use an area model or a simulation to calculate the expected value, as I stated above. Area models are diagrams or visual drawings, etc. to show exact percentages. Simulations are trials used to find the experimental probability by running an experiment.
4. Expected value is sometimes called the long-term average. Explain why this makes sense.
~ Expected value is the average. The long term average is the probability for something to occur. Data is necessary to support the expected value. The more trials that are conducted, the more accurate the data is. Testing something 100 times rather than 10 times will give you more accurate data.
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