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Name______________________________________________________________ Date_____________________ Class_______ REVIEW for EXAM Directions: Read and solve each question. Be sure to show your work. NO WORK = NO CREDIT Sample Space Sample Space QUESTION Things to remember… Sample Space shows all the possible outcomes of an event. The sample space can be shown as a TREE DIAGRAM or LIST. Example: Show the sample space for spinning the spinner and picking a marble. 1 9 There are 2 red marbles, 2 yellow marbles, and 1 purple marble in a bag. Sam picks 2 marbles from the bag. Which list shows all the possible unique outcomes? A Purple/red, purple/yellow, yellow/red, yellow/yellow, red/red B Purple/purple, purple/red, purple/yellow, yellow/red, yellow/yellow, red/red C Yellow/red, yellow/yellow, yellow/purple 3 7 5 D Purple/red, purple/yellow, yellow/red, yellow/purple, red/yellow, red/purple TREE DIAGRAM Spinner 1 3 5 7 9 LIST Marble 1, 1, 1, 1, 1, White Grey Striped Spotted Black 3, 3, 3, 3, 3, White Grey Striped Spotted Black Things to remember… 5, 5, 5, 5, 5, White Grey Striped Spotted Black The fraction form is White Grey Striped Spotted Black 7, 7, 7, 7, 7, White Grey Striped Spotted Black White Grey Striped Spotted Black 9, 9, 9, 9, 9, White Grey Striped Spotted Black White Grey Striped Spotted Black White Grey Striped Spotted Black White Grey Striped Spotted Black To determine the total possible outcomes… Count the combinations in the tree diagram Count the combinations in the list Use the Counting Principle… # of outcomes Event 1 x # of outcomes Event 2 5 x 5 = 25 total outcomes Probability and its Complement The probability of any event can be written as a fraction, decimal, or percent. Favorable outcomes Total outcomes The COMPLEMENT of any event is what is NOT included P(EVENT) + P(COMPLEMENT) = 1 Example: Find the probability of spinning blue and its complement. blue green red purple yellow P(blue) P(NOT blue) COMPLEMENT EVENT 1 5 + 4 5 = 5 5 or 1 Probability and its Complement QUESTION Which of the following correctly describes the relationship between the probability of rolling a 2 and the probability of its complement on a standard six-sided number cube? INDEPENDENT Example 2: Find the probability of picking two vowels, if you pick one card, replace it, then pick a second card. E X A M W D E N E S D A Y P(vowel, vowel) 5 5 25 x = 13 13 169 A The probabilities are equal. B The probabilities have a product of 1. C The probability of rolling a 2 is , and the probability of not rolling a 2 is . DEPENDENT Example: Find the probability of picking two striped marbles, if you pick one, then without replacing it, picking another. D The probability of rolling a 2 is less than the probability of not rolling a 2. P(striped, striped) 3 2 6 x = 90 10 9 Compound Events Things to remember… There are two types of compound events: Independent (replacing or separate events) o Find the probability of each event, then Compound Events QUESTION MULTIPLY Dependent (WITHOUT replacing) o Find the probability of each event, then MULTIPLY INDEPENDENT Example 1: Mary had a stack of 10 cards numbered 1-10. She randomly chooses two cards without replacing the first card. What is the probability that Mary chooses two composite numbers? Find the probability of flipping tails, spinning red, and picking a striped marble. A red blue B 2 9 1 4 because because 5 10 5 10 4 ∙ = 9 5 ∙ 10 = 20 90 25 100 yellow C P(tails, red, striped) 1 x 1 x 2 = 2 3 75 5 5 D 1 5 because 5 18 5 10 because 5 10 4 ∙ 10 ∙ 5 9 = = 20 100 25 90 Theoretical & Experimental Predictions Things to remember… Things to remember… Theoretical Probability – what SHOULD happen; normal probability Experimental Probability – what ACTUALLY happens; probability based on DATA To make a prediction using probability you must use a PROPORTION. Example: Jaylen rolled a fair number cube 100 times. He recorded his results below. Theoretical Probability QUESTION Noah has five cartons of orange juice, three cartons of apple juice, and two cartons of cranberry juice in his refrigerator. He takes out a carton at random and then another one without replacing the first. What is the theoretical probability that both cartons are of orange juice? Number on die 1 2 3 4 5 6 Times rolled 11 27 18 23 9 12 A If Jaylen rolls the die 250 times, about how many times should he expect to roll a 2 or 3? B First, find experimental probability. P(2 or 3) 45 100 C D Second, set up and solve a proportion. 45 = x 100 250 Experimental Probability QUESTION This is not a real question. You must keep reading and follow the directions. On a separate sheet of paper, you must write a note to your teacher listing the answer choices from greatest to least. If you turn it in before your exam, you may receive some extra credit points. A 250 B 125 C 200 D 375 45 x 250 = 11250 11250 ÷ 100 = 112.5 Jaylen should roll a 2 or 3 about 113 times. Predictions QUESTION Qualitative and Quantitative Things to remember… Aisha helps her mother at the family store. She has to decide how many of each kind of package of battery to sell in the store next week. The table shows how many packages of each kind of battery were sold yesterday. Qualitative data is information about QUALITITIES. This data canNOT be measured using numbers. Example: less likely, more likely, impossible Quantitative data is information about QUANTITIES. This data can be measured using numbers. Example: 54 inches, 12 feet, 33 days If Aisha's mother says to order 50 packages of batteries, how many packages of AA batteries should Aisha order? Qualitative and Quantitative QUESTION A bag contains only red and blue marbles. A 12 There are 6 marbles in the bag. B 13 The bag contains twice as many blue C 24 D 25 marbles as red marbles. Nadia draws a marble and replaces it. She repeats this process 18 times. What is the best prediction of the number times Nadia will draw a blue marble? A 4 times B 6 times C 10 times D 12 times