# LESSON 6 3 Making Predictions with Theoretical Probability

LESSON 6. 3 Making Predictions with Theoretical Probability How do you make predictions using theoretical probability?

ADDITIONAL EXAMPLE 1 A A spinner has eight equal sections numbered from 1– 8. Predict how many times the pointer will land on a multiple of 3 in 300 spins. about 75 B Blake volunteers at the animal shelter. He has an equally likely chance of being assigned to the dog, cat, bird, or reptile section. If he volunteers 30 times, about how many times should he expect to be assigned to the cat or reptile section? about 15 times

ADDITIONAL EXAMPLE 2 A Lea pulls a blue tile out of a bag of same-size tiles without looking. There are 4 purple tiles, 6 blue tiles, and 8 green tiles left in the bag. Find theoretical probability that the next tile she picks is the same color and the probability that it is a different color. Is it likely the next tile she picks will match?

ADDITIONAL EXAMPLE 2 B A company randomly assigns employees four-digit security codes using the numbers 1 through 4 to activate their e-mail accounts. Any of the digits can be repeated. Is it likely that more than 3 of the 1, 280 employees will be assigned the code 4113? Yes, it is likely that about five employees will be assigned the code 4113.

6. 3 LESSON QUIZ 7. 6. H 1. You roll a six-sided number cube 270 times. Predict how many times you will roll a number less than 3. about 90 times 2. The equal sections of a spinner have one of the following letters: A, B, A, C, B. Predict how many times the pointer will land on a consonant in 60 spins. about 36 times

3. In Kim’s homeroom, 4 students have no siblings, 9 students have 1 sibling, 8 students have 2 siblings, and 2 students have 3 or more siblings. Is it likely that a student chosen at random will have 2 or more siblings? Explain. 4. Drew rolls two number cubes 75 times. Is it likely that she will get a sum of 3 more than 5 times? Explain. No, it is likely she will get the sum about 4 times since

A probability model for an event gives all the possible outcomes of the event and the probabilities for that event. a. Use a table to create a probability model for drawing a card of any of the four equal suits using a standard deck of 52 cards. b. Each probability in a probability model must be between 0 and 1 inclusive. The total of the probabilities must be 1. Verify that these conditions are true for your model.

c. Josh draws a card randomly from a deck, records the suit, returns the card to the deck, and then shuffles the deck. He repeats this experiment 500 times. Explain how to use the probability model to predict about how many times Josh can expect to draw a card that is not a spade. Sample answer: The probability of a card that is not a spade is. In 500 draws there will be about 375 cards that are not spades.

How do you make predictions using theoretical probability? Sample answer: Use theoretical probability to write an equation or use a proportion to make the prediction for a given experiment.

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