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Example 6-5b Objective Find and compare experimental and theoretical probabilities

Example 6-5b Vocabulary Experimental probability An estimated probability based on the relative frequency of positive outcomes occurring during an experiment

Example 6-5b Vocabulary Theoretical probability The ratio of the number of ways an event can occur to the number of possible outcomes

Example 6-5b Vocabulary Sample space A set of all possible outcomes

Lesson 6 Contents Example 1Experimental Probability Example 2Experimental and Theoretical Probability Example 3Experimental and Theoretical Probability Example 4Predict Future Events Example 5Predict Future Events

Example 6-1a A spinner is spun 50 times, and it lands on the color blue 15 times. What is the experimental probability of spinning blue? Write probability statement P(blue) = 1/5 Replace numerator with 15 Replace denominator with 50 probability of Write probability formula spinning blue

Example 6-1a A spinner is spun 50 times, and it lands on the color blue 15 times. What is the experimental probability of spinning blue? P(blue) = 1/5 Find the GCF= 5 Divide GCF into numerator and denominator  5 P(blue) = Answer:

Example 6-1b A marble is pulled from a bag of colored marbles 30 times and 18 of the pulls results in a yellow marble. What is the experimental probability of pulling a yellow marble? Answer: P(yellow) = 1/5

Example 6-2a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Find the experimental probability of rolling a 5. 2/5 Write probability statement Find the experimental probability of rolling a 5 Write probability formula

Example 6-2a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Find the experimental probability of rolling a 5. 2/5 Find the experimental probability of rolling a 5 Replace numerator with 4 P(5) = 4 Replace denominator with 30 30

Example 6-2a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Find the experimental probability of rolling a 5. 2/5 Find the experimental probability of rolling a 5 P(5) = 4 30 Find the GCF= 2 Divide GCF into numerator and denominator  2 P(5) = 2 15 Answer:

Example 6-2b The graph shows the result of an experiment in which a coin was tossed 150 times. Find the experimental probability of tossing heads for this experiment. Answer: P(heads) = 2/5

Example 6-3a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Compare the experimental probability of rolling a 5 to its theoretical probability. Determine theoretical probability 3/5 Write probability statement probability of rolling a 5 Write probability formula

Example 6-3a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Compare the experimental probability of rolling a 5 to its theoretical probability. Determine theoretical probability 3/5 probability of rolling a 5 Replace numerator with 1 P(5) = Replace denominator with 6 since there are 6 numbers 1 6

Example 6-3a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Compare the experimental probability of rolling a 5 to its theoretical probability. Determine theoretical probability 3/5 probability of rolling a 5 P(5) = 1 6 You figured experimental probability for this data in Example 2, use it Determine experimental probability P(5) = 2 15

Example 6-3a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Compare the experimental probability of rolling a 5 to its theoretical probability. Theoretical probability 3/5 P(5) = 1 6 Experimental probability P(5) = 2 15 Convert each fraction to a decimal Exp P(5) = 0.13 P(5) = 0.17 Compare decimals by lining up decimals places The P(5) = 0.17 Answer: Theoretical probability is greater than experimental probability

Example 6-3b The graph shows the result of an experiment in which a coin was tossed 150 times. Compare the experimental probability of tossing heads to its theoretical probability. Answer: Theoretical probability is greater than experimental probability = 0.50 Theoretical Experimental = /5

Example 6-4a MOVIES In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story, 15 chose The Ink Well, 10 chose The Monkey House, and 5 chose Little Rabbit. What is the experimental probability of someone wanting to see The Monkey House? P(The Monkey House) = number of time The Monkey House chosen number of possible times chosen 4/5 Write probability statement Write probability formula experimental probability see The Monkey House

Example 6-4a MOVIES In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story, 15 chose The Ink Well, 10 chose The Monkey House, and 5 chose Little Rabbit. What is the experimental probability of someone wanting to see The Monkey House? P(The Monkey House) = number of time The Monkey House chosen number of possible times chosen P(The Monkey House) = 4/5 experimental probability see The Monkey House Replace numerator with 10 Replace denominator with 50

Example 6-4a MOVIES In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story, 15 chose The Ink Well, 10 chose The Monkey House, and 5 chose Little Rabbit. What is the experimental probability of someone wanting to see The Monkey House? P(The Monkey House) = number of time The Monkey House chosen number of possible times chosen P(The Monkey House) = 4/5 experimental probability see The Monkey House Find the GCF= 10 Divide GCF into numerator and denominator  10 P(The Monkey House) = 1 5 Answer:

Example 6-4b SPORTS In a survey, 100 people were asked to pick which sport they would watch on TV over the weekend. Thirty-five chose football, 20 chose basketball, 25 chose hockey, and 20 chose soccer. What is the experimental probability of someone wanting to watch football? Answer: P(football) = 4/5

Example 6-5a In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story, 15 chose The Ink Well, 10 chose The Monkey House, and 5 chose Little Rabbit. Suppose 300 people are expected to attend a movie theater this weekend to see one of the four movies. How many can be expected to see The Monkey House? Write a proportion Use the probability for The Monkey House from example 4 5/5 are expected to attend Suppose 300 people 300 are expected to attend (total) Define variable

Example 6-5a Find the cross products. 5x = 1(300) 5x = 300 Multiply 55 5x = 1(300) 5x = 300 5/5 Ask “what is being done to the variable?” The variable is being multiplied by 5 Using the fraction bar, divide both sides by 5 Bring down 5x = 300 Do the inverse on both sides of the equal sign

Example 6-5a Combine “like” terms 5x = 1(300) 5x = x = 1(300) 5x = 300 5/5 1  x = 60 Use the Identity Property of Multiplication to multiply 1  x x = 60 Add dimensional analysis How many can be expected to see The Monkey House? people see Monkey House Answer:

Example 6-5b In a survey, 100 people were asked to pick which sport they would watch on TV over the weekend. Thirty-five chose football, 20 chose basketball, 25 chose hockey, and 20 chose soccer. Suppose 1,500 people are expected to watch sports on TV this weekend. How many can be expected to watch football? Answer: x = 525 people watch football * 5/5

End of Lesson 6 Assignment Lesson 9:6Theoretical and Experimental All Probability