4-1 Basic Concepts of Probability 147 those that are approximations, so an instruction to “find the probability” could actually mean “estimate the probability.” 2. Classical Approach to Probability (Requires Equally Likely Outcomes) If a procedure has n different simple events that are equally likely, and if event A can occur in s different ways, then P1A2 = number of ways A occurs number of different simple events = s n 3. Subjective Probabilities P1A2, the probability of event A, is estimated by using knowledge of the relevant circumstances. Figure 4-3 illustrates the approaches of the preceding three definitions. FIGURE 4-3 Three Approaches to Finding a Probability 1. Relative Frequency Approach: When trying to determine the probability that an individual car crashes in a year, we must examine past results to determine the number of cars in use in a year and the number of them that crashed; then we find the ratio of the number of cars that crashed to the total number of cars. For a recent year, the result is a probability of 0.0480. (See Example 3.) 2. Classical Approach: When trying to determine the probability of winning the grand prize in a lottery by selecting six different numbers between 1 and 60, each combination has an equal chance of occurring. The probability of winning is 0.0000000200, which can be found by using methods presented in Section 4-4. (See Example 4.) 3. Subjective Probability: When trying to estimate the probability of getting stuck in the next elevator that you ride, we know from personal experience that the probability is quite small. Let’s estimate it to be, say, 0.001 (equivalent to 1 chance in 1000). (See Example 5.) CAUTION When using the classical approach, always confirm that the outcomes are equally likely.
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