104 Theoretical Probability


 Reynold Rice
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1 Problem of the Day A spinner is divided into 4 different colored sections. It is designed so that the probability of spinning red is twice the probability of spinning green, the probability of spinning blue is 3 times the probability of spinning green, and the probability of spinning yellow is 4 times the probability of spinning green. What is the probability of spinning yellow? 0.4
2 Pg. 540 Learn to estimate probability using theoretical methods.
3 Theoretical probability is used to estimate probabilities by making certain assumptions about an experiment. Suppose a sample space has 5 outcomes that are equally likely, that is, they all have the same probability, x. The probabilities must add to 1. x + x + x + x + x = 1 5x = 1 x = 1 5
4 A coin, die, or other object is called fair if all outcomes are equally likely.
5 An experiment consists of spinning this spinner once. Find the probability of the event. Leave the answer in fraction form. P(4) The spinner is fair, so all 5 outcomes are equally likely: 1, 2, 3, 4, and 5. P(4) = number of outcomes for 4 = 5 1 5
6 Example 1: An experiment consists of spinning this spinner once. Find the probability of the event. Leave the answer in fraction form. P(even number) for answer move square to the right 2 5
7 Example 2: An experiment consists of spinning this spinner once. Find the probability of the event. Leave the answer in fraction form. P(1) for answer move square to the right 1 5 for answer move square to the right P(1 or an even #) 3 5
8 An experiment consists of rolling one fair number cube and flipping a coin. Find the probability of the event. Show a sample space that has all outcomes equally likely. The outcome of rolling a 5 and flipping heads can be written as the ordered pair (5, H). There are 12 possible outcomes in the sample space. 1H 2H 3H 4H 5H 6H 1T 2T 3T 4T 5T 6T
9 Example 3: An experiment consists of flipping two coins. Find the probability of the event. Leave the answer in fraction form. P(one head & one tail) List all the possible outcome in the sample space: P(head and tail) = for answer move square to the right 1 2
10 Example 4: An experiment consists of flipping two coins. Find the probability of the event. Leave the answer in fraction form. P(both tails) P(both tails) = for answer move square to the right 1 4
11 Stephany has 2 dimes and 3 nickels. How many pennies should be added so that the probability of drawing a nickel is 3? x = 3 7 Set up a proportion. 3(5 + x) = 3(7) Find the cross products. Solve. 2 pennies should be added to the bag.
12 Example 5: Carl has 3 green buttons and 4 purple buttons. How many white buttons should be added so that the probability of drawing a purple button is 2? 9 Adding buttons to the bag will increase the number of possible outcomes. Let x equal the number of white buttons. Set up a proportion x = 2 9 Find the cross products. 2(7 + x) = 9(4) Solve. x = 11
13 Two events are mutually exclusive, or disjoint events, if they cannot both occur in the same trial of an experiment. For example, rolling a 5 and an even number on a number cube are mutually exclusive events because they cannot both happen at the same time. Suppose both A and B are two mutually exclusive events. P(both A and B will occur) = 0 P(either A or B will occur) = P(A) + P(B)
14 Suppose you are playing a game in which you roll two fair number cubes. If you roll a total of five you will win. If you roll a total of two, you will lose. If you roll anything else, the game continues. What is the probability that you will lose on your next roll? The event total = 2 consists of 1 outcome, (1, 1), so (total = 2) = The probability that you will lose is 1, or about 3%. 36
15 Example 6: An experiment consists of rolling two fair number cubes. Find the probability of each event. a.) P(total shown = 8) b.) P(total shown > 9) c.) P(at least one 3)
16 Homework #24 Lesson 10.4 Pg. 543 (1 24 ALL) Check your odd answers at home in the back of the book with a red pen!
17
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