134 CHAPTER 3 Probability Types of Probability The method you will use to calculate a probability depends on the type of probability. There are three types of probability: classical probability, empirical probability, and subjective probability. The probability that event E will occur is written as P1E2 and is read as “the probability of event E.” Classical (or theoretical) probability is used when each outcome in a sample space is equally likely to occur. The classical probability for an event E is given by P1E2 = Number of outcomes in event E Total number of outcomes in sample space . DEFINITION Finding Classical Probabilities You roll a six-sided die. Find the probability of each event. 1. Event A: rolling a 3 2. Event B: rolling a 7 3. Event C: rolling a number less than 5 SOLUTION When a six-sided die is rolled, the sample space consists of six outcomes: 51, 2, 3, 4, 5, 66. Because each outcome in the sample space is equally likely to occur, you can use the formula for classical probability. 1. There is one outcome in event A = 536. So, P1rolling a 32 = 1 6 ≈ 0.167. Round to three decimal places. The probability of rolling a 3 is 1 6, or about 0.167. 2. Because 7 is not in the sample space, there are no outcomes in event B. So, P1rolling a 72 = 0 6 = 0. Event is not possible. The probability of rolling a 7 is 0, so it is not possible for the event to occur. 3. There are four outcomes in event C = 51, 2, 3, 46. So, P1rolling a number less than 52 = 4 6 = 2 3 ≈ 0.667. The probability of rolling a number less than 5 is 2 3, or about 0.667. TRY IT YOURSELF 5 You select a card from a standard deck of playing cards (see figure). Find the probability of each event. 1. Event D: Selecting the nine of clubs 2. Event E: Selecting a heart 3. Event F: Selecting a diamond, heart, club, or spade Answer: Page A38 EXAMPLE 5 A K Q J 10 9 8 7 6 5 4 3 2 A K Q J 10 9 8 7 6 5 4 3 2 A K Q J 10 9 8 7 6 5 4 3 2 A K Q J 10 9 8 7 6 5 4 3 2 Spades Diamonds Hearts Clubs Standard Deck of Playing Cards Study Tip Probabilities can be written as fractions, decimals, or percents. In Example 5, the probabilities are written as reduced fractions and decimals, with decimals rounded to three places when possible. For very small probabilities, round to the first nonzero digit. For example, 0.0000271 would be 0.00003. In general, these round-off rules will be used throughout the text. (Note that some results may be rounded differently for accuracy.)
RkJQdWJsaXNoZXIy NjM5ODQ=