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California Standards. SDAP3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven). Also covered: SDAP3.3. Vocabulary. experimental probability.
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California Standards SDAP3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven). Also covered:SDAP3.3
Vocabulary experimental probability
Experimental probability is one way of estimating the probability of an event. The experimental probability of an event is found by comparing the number of times the event occurs to the total number of trials when repeating an experiment many times. The more trials you have, the more accurate the estimate is likely to be.
number of times an event occurs total number of trials P(event) number of jumps landed number of jumps attempted P(jumps landed) ≈ 0.583 ≈ 58.3% 7 12 = Additional Example 1: Sports Application During skating practice, Sasha landed 7 out of 12 jumps. What is the experimental probability that she will land her next jump? Write your answer as a ratio, as a decimal, and as a percent. Then explain why your answer is reasonable. Substitute data from the experiment. Write as a decimal and as a percent.
The experimental probability that Sasha will land her next jump is or 0.583, or 58.3%. 7 12 Sasha landed about half, or 50%, of the 12 jumps, so an answer of 58.3% is reasonable. Additional Example 1 Continued During skating practice, Sasha landed 7 out of 12 jumps. What is the experimental probability that she will land her next jump? Write your answer as a ratio, as a decimal, and as a percent. Then explain why your answer is reasonable.
Writing Math “P(event)” represents the probability that an event will occur. For example, the probability of a flipped coin landing heads up could be written as “P(heads).”
number of times an event occurs total number of trials P(event) number of free throws made number of free throws attempted P(free throws made) 9 10 = Check It Out! Example 1 During basketball practice, Martha made 9 out of 10 free throws. What is the experimental probability that she will make her next attempt? Write your answer as a ratio, as a decimal, and as a percent. Then explain why your answer is reasonable. Substitute data from the experiment and write as a percent. Write as a decimal and as a percent. = 0.9 = 90%
The experimental probability that Martha will make the next free throw is , or 0.9, or 90%. 9 10 Check It Out! Example 1 Continued During basketball practice, Martha made 9 out of 10 free throws. What is the experimental probability that she will make her next attempt? Write your answer as a ratio, as a decimal, and as a percent. Then explain why your answer is reasonable. Martha made almost all, or 100%, of the 10 free throws, so an answer of 90% is reasonable.
The experimental probability that the next book checked out will be fiction is 32 55 . Additional Example 2: Application Students have checked out 55 books from the library. Of these, 32 books are fiction. A. What is the experimental probability that the next book checked out will be fiction? number of fiction books checked out total number of books checked out P(fiction) 32 55 Substitute data. =
32 55 Subtract from both sides. 32 55 –=– _______________________________ 32 55 23 55 . Additional Example 2: Application Students have checked out 55 books from the library. Of these, 32 books are fiction. B. What is the experimental probability that the next book checked out will be nonfiction? P(fiction) + P(nonfiction) = 1 Use the complement. 32 55 + P(nonfiction) = 1 Substitute. 23 55 P(nonfiction) = The experimental probability that the next book checked out will be nonfiction is approximately
number of pears selected total number of fruit selected P(pear) 18 47 . Check It Out! Example 2 Students have a fruit choice of either an apple or a pear. So far 18 of 47 students have selected pears. A. What is the experimental probability that the next fruit selected will be a pear? 18 47 Substitute data. = The experimental probability that the next fruit selected will be a pear is
18 47 Subtract from both sides. 18 47 18 47 –=– __________________________ 29 47 . Check It Out! Example 2 Students have a fruit choice of either an apple or a pear. So far 18 of 47 students have selected pears. B. What is the experimental probability that next fruit selected will be an apple? P(pear) + P(apple) = 1 Use the complement. 18 47 Substitute. + P(apple) = 1 29 47 P(apple) = The experimental probability that the next fruit selected will be an apple is
