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# Lesson 11 3 theoretical probability

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### Lesson 11 3 theoretical probability

1. 1. Name ____________________________________ Date ______________________Mrs. Labuski & Mrs. Rooney Period ______ Lesson 11-3 Theoretical Probability VOCABULARY DEFINITION EXAMPLETheoreticalProbability Equally likely Fair
2. 2. Finding Theoretical ProbabilityWhat is the probability that a fair coin will and heads up? number or ways event can occurP(heads) = Total number of possible outcomesThere are ________ outcomes: _______________ and _____________ number or ways event can occurP(heads) = 2 possible outcomesThere is only one way for the coin to land heads up 1 way event can occur =P(heads) = 2 possible outcomesWhat is the probability of rolling a number less than 5 on a fair number cube? number or ways event can occurP(number less than 5) = Total number of possible outcomesThere are six outcomes: ____________________________P(number less than 5) = number or ways event can occur 6 possible outcomesThere four ways to roll less than 5: ________________________P(number less than 5) = 4 way event can occur = 6 possible outcomesFinding the probabilities of Events Not HappeningTo find the probability of an event not happening, find the probability that it willhappen and subtract from 100%.Suppose there is a 10% chance that it will rain tonight. What is the probability thatit will not rain?P(rain) + P(not rain)=100% + P(not rain)= 100%
3. 3. Find the probability of each event using the spinner.1. landing on blue ___________________2. landing on red____________________3. landing on green _________________4. not landing on blue ________________Find the probability of each event using the bag of marbles.5. picking a black marble ________________6. picking a striped marble ________________7. picking a white marble ________________8. not picking a white marble ________________A standard number cube is rolled. Find each probability.9. P(2) ________________ 10. P(even number) ________________11. P(4 or 5) ________________ 12. P(odd number) ________________13. Out of 10 fair coin tosses, a coin landed tails up 4 times. How does thisexperimental probability of a fair coin landing tails up compare to the theoreticalprobability of the same event?____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________14. The probability of a spinner landing on blue is ¾. What is the probability of itnot landing on blue written as a percent?
4. 4. A standard number cube is rolled. Find each probability1. P(5) ________________ 2. P(1, 2, or 3) ________________3. P(1 or 4) ________________ 4. P(negative number) ________________5. P(even number) ____________ 6. P(odd number) ________________7. P(positive number) ___________ 8. P(number less than 3) _______________9. P(not 2) ________________ 10. P(not 3 or 4) ________________Seven pieces of paper with the numbers 1, 2, 3, 4, 4, 5, and 6 printed on themare placed in a bag. A student chooses one without looking. Compare theprobabilities. Write <, >, or = .11. P(1) ______P(5) 12. P(2) ________P(4)13. P(4 or 5) _______P(1 or 3) 14. P(less than 4) _______P(greater than 3)15. Explain why this spinner could not be used for a fair experiment.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________16. There is a 62% chance of rain tomorrow and a 19% chance of sleet. What is theprobability that neither event will occur?
5. 5. Name _____________________________ Date ______________________Mrs. Labuski & Mrs. Rooney Per ______ Lesson 11-3 Theoretical Probability VOCABULARY DEFINITION EXAMPLE Probability whenTheoretical all outcomes have Theoretical probability ≈ number or ways event can occur the same chance of Total number of possible outcomesProbability occurring When all Equally outcomes have the likely same chance of occurring An experiment Fair with equally likely outcomes
6. 6. Finding Theoretical Probability What is the probability that a fair coin will and heads up? number or ways event can occur P(heads) = Total number of possible outcomes There are 2 outcomes: heads and tails number or ways event can occur P(heads) = 2 possible outcomes There is only one way for the coin to land heads up 1 way event can occur = 1 P(heads) = 2 possible outcomes 2 What is the probability of rolling a number less than 5 on a fair number cube?P(number less than 5) = number or ways event can occur Total number of possible outcomes There are six outcomes: 1,2,3,4,5,6 P(number less than 5) = number or ways event can occur 6 possible outcomes There four ways to roll less than 5: 1,2,3,4P(number less than 5) = 4 way event can occur = 4 = 2 6 possible outcomes 6 3 Finding the probabilities of Events Not Happening To find the probability of an event not happening, find the probability that it will happen and subtract from 100%. Suppose there is a 10% chance that it will rain tonight. What is the probability that it will not rain? P(rain) + P(not rain)=100% 10% + P(not rain)= 100% -10% -10% P(not rain)= 90%
7. 7. Find the probability of each event using the spinner.1. landing on blue 3/52. landing on red 1/53. landing on green 1/54. not landing on blue 2/5Find the probability of each event using the bag of marbles.5. picking a black marble 4/96. picking a striped marble 1/37. picking a white marble 2/98. not picking a white marble 7/9A standard number cube is rolled. Find each probability.9. P(2) 1/6 10. P(even number) 3/6 = ½11. P(4 or 5) 2/6 = 1/3 12. P(odd number) 3/6 = ½13. Out of 10 fair coin tosses, a coin landed tails up 4 times. How does thisexperimental probability of a fair coin landing tails up compare to the theoreticalprobability of the same event?experimental probability = 4/10 = 40% theoretical probability = ½ =50%The experimental probability is 40%, which is less than the theoretical probability which is 50%.14. The probability of a spinner landing on blue is ¾. What is the probability of itnot landing on blue written as a percent? ¼ = 25%
8. 8. A standard number cube is rolled. Find each probability1. P(5) 1/6 2. P(1, 2, or 3) 3/6 = ½3. P(1 or 4) 1/3_____________ 4. P(negative number) 05. P(even number) 3/6 = ½ ______ 6. P(odd number) 3/6 = ½7. P(positive number) 1 or 100% 8. P(number less than 3) 1/39. P(not 2) 5/6 10. P(not 3 or 4) 4/6 = 2/3Seven pieces of paper with the numbers 1, 2, 3, 4, 4, 5, and 6 printed on themare placed in a bag. A student chooses one without looking. Compare theprobabilities. Write <, >, or = .11. P(1) = P(5) 12. P(2) < P(4) 1 1 1 2 7 7 7 713. P(4 or 5) > P(1 or 3) 14. P(less than 4) > P(greater than 3) 3 2 3 4 7 7 7 715. Explain why this spinner could not be used for a fair experiment.There is a greater chance of the spinner landing on red than on any other colorbecause there are two red sections and only one section ofevery other color.16. There is a 62% chance of rain tomorrow and a 19% chance of sleet. What is theprobability that neither event will occur? 62% 100% + 19% -81% 19% 81% 19%