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Understanding Probability Concepts and Practice Activities

Learn about probability terms, sample spaces, tree diagrams, and warm-up exercises to enhance your understanding of probability. Practice picking vowels, numbers, and outcomes to strengthen your skills. Explore various scenarios and equations related to probability calculations.

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Understanding Probability Concepts and Practice Activities

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  1. Warm-Ups

  2. Probability

  3. Probability Terms • Probability- how likely something will happen • Outcome- result of an action • Event- collection of possible outcomes • Complement- collection of outcomes not contained in the event Formula: number of favorable outcomes total number of possible outcomes

  4. Probability • Between 0 and 1 • Can be written as a fraction, decimal or percent • The closer to one a number is, the more likely the event will occur

  5. Probability Terms • Vowel: letters A, E, I, O, U • Consonant: the remaining 21 letters • Even #s: 2, 4, 6, 8, 10… • Odd #s: 1, 3, 5, 7, 9, 11… • Multiples: count by that # • Die: 1 number cube • Dice: 2 or more number cubes

  6. Practice B • Probability of picking a vowel: • Probability of picking a red chip: • Probability of picking a consonant: A C D E

  7. Practice- Use 1 number cube • P(even number) • P(odd number) • P(larger than 2) • P(less than 4)

  8. Sample Spaces • Collection of all possible outcomes • Make a table to organize your data • Create a table for all possibilities for rolling 2 number cubes

  9. Outcomes from 2 dice

  10. Tree Diagrams Suppose you are going to travel on a river. You have two choices of boats—a kayak or a rowboat. You can go upstream on three smaller streams, to the north, northwest and northeast. What is the sample space for your journey?

  11. Tree Diagram North Sample Space: KN, KNW, KNE, RN, RNW, RNE Northwest Kayak Northeast North Northwest Rowboat Northeast

  12. Make a tree diagram for tossing a coin three times. Heads Sample Space: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT Heads Tails Heads Heads Tails Tails Heads Heads Tails Tails Heads Tails Tails

  13. Warm-Ups • The square root of 127 is between what two numbers? • Convert 3/7 to a decimal and a percent.

  14. Hair Color • How many people are in the group? • Find the probability of having brown hair. • Find the probability of not having black hair.

  15. Warm-Ups • y + 10.2 = 12 • g – 5 = -9.4 • Fingernails grow about 1.5 inches per year. How long would it take to grow nails 37 inches long?

  16. Warm-Ups • 10k + 20 = 100 • Find the mean, median, mode and range: 5, 9, 2, 10, 15, 5 • What is the 12th term of the sequence 6n-5 where n represents the position of a term in the sequence?

  17. Which problem situation matches the equation 2 + 5 + 6 = x? • Petra is 2 years old, Anja is 5 years old and Heinz is 6 years old. Find x, the average age of these three children. • Diana has 2 pennies, 5 dimes and 6 nickels. Find x, the total amount of money Diana has. • The can opener uses 2 amps, the toaster uses 5 amps and the microwave oven uses 6 amps. Find x, the total amps all will use if operated at the same time. • Joshua has 6 play shirts. Of these, he can use 2 as dress shirts. Including those 2, he has 5 dress shirts. Find x, the total number of shirts Joshua has.

  18. Esther is paid $0.50 a page plus $2 an hour for typing research papers for college students. Which equation could be used to determine the number of pages x she typed if it took her 6 hours and her fee was $34? • 0.5x + 2(6) = 34 • 2x + 0.5(6) = 34 • 2(6 + 0.5x) = 34 • 0.5x + 6 = 34 • 2x + 50(6) = 34

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