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Algebra III Academic Introduction to Probability Calculate probability Understand the basic counting principles Probability: Random Experiment: Outcome: Event: Sample Space: Probability of an event - # outcomes in the event # of outcomes in the sample space The value of a probability must be between _______ and ________ . Outcomes of rolling two dice: White / Black 1 2 3 4 5 6 1 2 3 4 5 6 Example #1 A pair of dice is rolled. There is one black die and one white die. Find the probability of each of the following events: 1. The total is 10. 2. The total is at least 10. 3. The total is less than 10. 4. The total is at most 10. 5. The total is 7. 6. The total is 2. 7. The total is between 3 and 7, inclusive. 9. The total is between 2 and 12, inclusive. 8. The total is between 3 and 7. 10. The total is 13. 11. The numbers are 2 and 5. 12. The black die has 2 and the white die has 5. 13. The black die has 2 or the white die has 5. Counting Principles We do not want to list everything every time. 1.) When event A and event B are performed. So you do one and then the other. n(A and then B) = n(A) * n(B) 2.) The other is when Event A or Event B is performed. So you do one or the other. n(A or B) = n(A) + n(B) “And” Means: “Or” Means: Example #2 A. Using only the letters in SEQUOIA: a. In how many ways could you select a vowel and a consonant? b. In how many ways could you select a vowel or a consonant? c. How many different four-letter “words” could you form using no letter more than once in any given word? B. Nine people on a baseball team are trying to decide who will be which position. a. In how many different ways could they select a person to be pitcher? b. After someone has already been selected as pitcher, how many different ways could they select someone else to be catcher? c. In how many different ways could they select a pitcher and a catcher? d. After the pitcher and catcher have been selected, in how many ways could they select a first baseman? e. In how many different ways could they select a pitcher, a catcher, and a first baseman? You Try 1. A card is drawn at random from a normal 52-card deck. a. What name is given to the act of drawing the card? b. How many outcomes are there in the sample space? c. How many outcomes are there in the event, “The card is a face card?” d. Calculate P(The card is black). e. Calculate P(The card is a face card). f. Calculate P(The card is an Ace). g. Calculate P(The card is between 3 and 7, inclusive). h. Calculate P(The card is an 8 of clubs). 2. Ward Robe has 15 pairs of slacks and 23 shirts. In how many different ways could he select a slacks-andshirt combination? 3. A pizza establishment offers 12 kinds of meat toppings and 5 kinds of vegetable toppings. In how many different ways could you select: a. A meat topping or a vegetable topping? b. A meat topping and a vegetable topping?