~ 8.5 ~
More Estimating Probabilities
Learning Targets
I can calculate the probability of an event when the outcomes in the sample space are not equally likely.
I can explain why results from repeating an experiment may not exactly match the expected probability for an event.
Notes
A probability for an event represents the proportion of the time we expect that event to occur in the long run. For example, the probability of a coin landing heads up after a flip is ½, which means that if we flip a coin many times, we expect that it will land heads up about half of the time.
Even though the probability tells us what we should expect if we flip a coin many times, that doesn't mean we are more likely to get heads if we just got three tails in a row. The chances of getting heads are the same every time we flip the coin, no matter what the outcome was for past flips.
Activities
5.1 Is It Likely?
If the weather forecast calls for a 20% chance of light rain tomorrow, would you say that it is likely to rain tomorrow?
If the probability of a tornado today is ⅒, would you say that there will likely be a tornado today?
If the probability of snow this week is 0.85, would you say that it is likely to snow this week?
5.4 The Probability of Spinning B
Jada, Diego, and Elena each use the same spinner that has four (not necessarily equal sized) sections marked A, B, C, and D.
Jada says, "The probability of spinning B is 0.3 because I spun 10 times, and it landed on B 3 times."
Diego says, "The probability of spinning B is 20% because I spun 5 times, and it landed on B once."
Elena says, "The probability of spinning B is 2/7 because I spun 7 times, and it landed on B twice."
Based on their methods, which probability estimate do you think is the most accurate? Explain your reasoning.
Andre measures the spinner and finds that the B section takes up ¼ of the circle. Explain why none of the methods match this probability exactly.
Add to Your Notes
A student repeats the process of taking blocks out of a bag and replacing them 100 times. A green block is drawn 67 times. What is a good estimate for the probability of drawing out a green block from the bag?
67/100
A chance experiment is done a few times and the fraction of outcomes in a certain event is used as an estimate for the probability of the event. If the experiments are done carefully, how could the estimate be improved?
Usually, the more trials done for an experiment, the closer the estimate will be to a computed probability.
A chance experiment is repeated many times, but the fraction of outcomes for which a certain event occurs does not match the actual probability of the event. What are some reasons this may happen?
The experiment may not have been repeated enough times.
The experiment may not have been as random as originally thought.
Assignment
Check Google Classroom!