SECTION 3.1 Basic Concepts of Probability and Counting 137 The third type of probability is subjective probability. Subjective probabilities result from intuition, educated guesses, and estimates. For instance, given a patient’s health and extent of injuries, a doctor may feel that the patient has a 90% chance of a full recovery. Or a business analyst may predict that the chance of the employees of a certain company going on strike is 0.25. Classifying Types of Probability Classify each statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. 1. The probability that you will get an A on your next test is 0.9. 2. The probability that a voter chosen at random will be younger than 35 years old is 0.3. 3. The probability of winning a 1000-ticket raffle with one ticket is 1 1000. SOLUTION 1. This probability is most likely based on an educated guess. It is an example of subjective probability. 2. This statement is most likely based on a survey of a sample of voters, so it is an example of empirical probability. 3. Because you know the number of outcomes and each is equally likely, this is an example of classical probability. TRY IT YOURSELF 8 Based on previous counts, the probability of a salmon successfully passing through a dam on the Columbia River is 0.85. Is this statement an example of classical probability, empirical probability, or subjective probability? (Source: Army Corps of Engineers) Answer: Page A38 A probability cannot be negative or greater than 1, as stated in the rule below. The probability of an event E is between 0 and 1, inclusive. That is, 0 … P1E2 … 1. Range of Probabilities Rule When the probability of an event is 1, the event is certain to occur. When the probability of an event is 0, the event is impossible. A probability of 0.5 indicates that an event has an even chance of occurring or not occurring. The figure below shows the possible range of probabilities and their meanings. 0 Even chance Unlikely Likely Impossible Certain 1 0.5 0.75 0.25 An event that occurs with a probability of 0.05 or less is typically considered unusual. Unusual events are highly unlikely to occur. Later in this course you will identify unusual events when studying inferential statistics. EXAMPLE 8 For help with double inequalities, see Integrated Review at MyLab Statistics
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