10.2 Theoretical Probability and its Complement
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- Jewel Gallagher
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1 warm-up after A traveler can choose from 3 airlines, 5 hotels and 4 rental car companies. How many arrangements of these services are possible? 2. Your school yearbook has an editor and assistant editor. 15 students are on the yearbook staff. In how many ways can the students be chosen for these positions? 10.2 Theoretical Probability and its Complement Learning Target: I can calculate the theoretical probability and find its complement [S-CP.1] 1
2 If the outcomes in a sample space are equally likely to occur, then the probability of the event is a numerical value from to. equally likely to occur or not occur P(event) = number of favorable outcomes number of possible outcomes decimal During this unit, we will be writing probability as a (round to 3 decimal places) Theoretical Probability - The likelihood of an event based on what mathematically should happen. Use the spinner to find each theoretical probability. Write as a fraction and as a decimal rounded to 3 decimal places. 1. P(5) = sample space: or # of poss. outcomes = 2. P(an even number) = or 3. P(a number greater than 4) = or 4. P(a multiple of 3) = 5. P(NOT a multiple of 3) = or (theoretical)
3 Complement of an event - all of the possible outcomes in the sample space that are NOT part of the event. P(not event) = number of not favorable outcomes number of possible outcomes So, if... P(event) + P(not event) = then... P(not event) = EX: If P(yellow) = 0.7, then P(NOT yellow) = A bag contains letter tiles that spell the word M I S S I S S I P P I. Find the theoretical probability of drawing one tile at random for each of the following. Write answer as a fraction as a decimal rounded to 3 places. sample space: # of poss. outcomes = 6. P(M) = 7. P(not M) = 8. P(S) = 9. P(not S) = q = = 3
4 Moline High School has 534 freshmen, 554 sophomores, 546 juniors and 494 seniors. What is the probability that a student picked at random is a senior = 11. not a freshman = 12. an underclassman = EXIT 1. What is the sample space? 2. What is the number of possible outcomes? 3. P(A) = 4. P(not E) = 5. P(C) = 6. P(D) = 7. P( a letter) = Assignment: 10.2 Worksheet 4
5 Geometry 10.2 Day 1 Theoretical Probability, Complement Name Pd 1. If the probability of an event occurring is!, then the probability of that even NOT occurring is.! 2. If P A =!, then P not A =. 3. If P A = 0.35, then P not A =.! **When finding the probability, write the answer as a fraction and then a decimal rounded to 3 decimal places** 4. Use the spinner at the right to find the probability of the following: a. What is the sample space of this spinner? b. What is the number of possible outcomes? c. P(1) = d. P(4) = e. P(5) = f. P(less than 5) = g. P(even number) = h. P (not 2) = i. P (not 3) = Use for #1 5. You have a jar of change at home that contains 56 pennies, 72 nickels, 80 dimes and 64 quarters. a. What is the sample space of the jar? b. What is the total number of possible outcomes? c. P (drawing a dime) = d. P (not drawing a dime) = e. P (drawing a penny or nickel) = f. P (not drawing a quarter) = 6. Each of the letters in the word SUMMER are on separate cards, face down on the table. a. What is the total number of possible outcomes? b. If you pick a card at random, what is the probability that its letter will be an M? c. If you pick a card at random, what is the probability that its letter will NOT be an M? d. If you pick a card at random, what is the probability that its letter is not a vowel?
6 **When finding the probability, write the answer as a fraction and then a decimal rounded to 3 decimal places** 7. You ask a friend to pick a number from 1 to 10. a. What is the probability that your friend will pick 9? b. What is the probability that your friend will not pick a number less than 5? c. What is the probability that your friend will pick an odd number? d. What is the probability that your friend will pick a number that is at least 7? 8. A gumball machine contains 14 orange gumballs, 16 red gumballs, and 19 green gumballs. a. What is the probability that the next gumball that comes out will be orange? b. What is the probability that the next gumball will not be red? 9. You cannot decide what to wear to school. You have black or tan shorts. You also have a red, white or blue shirt. a. What is your sample space of outfits? (list all possible outfits) b. What is the total possible number of outfits? c. What is the probability of wearing the red shirt? d. What is the probability of wearing the black shorts? e. What is the probability of wearing the tan shorts with the white shirt? Extra Credit: 10. You draw one card out of a fair 52-card deck. A. What is the probability of drawing a red card? B. What is the probability of drawing a spade? C. What is the probability of drawing the Queen of Hearts? D. What is the probability of drawing an Ace?
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