~ 8.5 ~

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.

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.

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."

1. Based on their methods, which probability estimate do you think is the most accurate? Explain your reasoning.
2. 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.