SECTION 3.3 The Addition Rule 161 A Summary of Probability Type of probability and probability rules In words In symbols Classical Probability The number of outcomes in the sample space is known and each outcome is equally likely to occur. P1E2 = Number of outcomes in event E Number of outcomes in sample space Empirical Probability The frequency of each outcome in the sample space is estimated from experimentation. P1E2 = Frequency of event E Total frequency = f n Range of Probabilities Rule The probability of an event is between 0 and 1, inclusive. 0 … P1E2 … 1 Complementary Events The complement of event E is the set of all outcomes in a sample space that are not included in E, and is denoted by E′. P1E′2 = 1 - P1E2 Multiplication Rule The Multiplication Rule is used to find the probability of two events occurring in sequence. P1A and B2 = P1A2 # P1B0 A2 Dependent events P1A and B2 = P1A2 # P1B2 Independent events Addition Rule The Addition Rule is used to find the probability of at least one of two events occurring. P1A or B2 = P1A2 + P1B2 - P1A and B2 P1A or B2 = P1A2 + P1B2 Mutually exclusive events Combining Rules to Find Probabilities Use the figure at the right to find the probability that a randomly selected draft pick is not a running back or a wide receiver. SOLUTION Define events A and B. A: Draft pick is a running back. B: Draft pick is a wide receiver. These events are mutually exclusive, so the probability that the draft pick is a running back or wide receiver is P1A or B2 = P1A2 + P1B2 = 16 255 + 37 255 = 53 255 . By taking the complement of P1A or B2, you can determine that the probability of randomly selecting a draft pick who is not a running back or wide receiver is 1 - P1A or B2 = 1 - 53 255 = 202 255 ≈ 0.792. TRY IT YOURSELF 5 Find the probability that a randomly selected draft pick is not a linebacker or a quarterback. Answer: Page A38 EXAMPLE 5 (Source: National Football League) NFL Rookies A breakdown by position of the 255 players picked in the 2020 NFL draft: Quarterbacks Running backs Offensive tackles Guards Centers Tight ends Wide receivers Defensive ends Defensive backs Linebackers Defensive tackles 17 22 37 27 Kickers Punters 3 2 50 28 19 9 12 13 16
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