Long-time friends, Pat and Tom, agree on many things, but not the outcome of the American League pennant race and the World Series. Pat is originally from Boston, and Tom is from New York. They have a steak dinner bet on next year's race, with Pat betting on the Red Sox and Tom on the Yankees. Both are convinced they will win. What probability assessment technique is being used by the two friends?

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BlackTom AI · Accepted Answer

Consider the scenario: two long-time friends with a personal bet on the outcome of a future event (the baseball pennant race and World Series), each believing their side will win based on personal judgment rather than long-run data. This sets the stage for a probability assessment based on personal beliefs or opinions rather than objective data.
Option 1: Independent probability. This would involve probabilities derived from a model assuming outcomes are independent and typically using known frequencies or combinatorial calculations. In this case, there is no stated independent model or frequency data; the bet is not computed from counts of past seasons or combinatorial enumeration, so this option does not fit.
Option 2: Subjective probability. This fits well: Pat and Tom are forming beliefs about future events (which team will win) based on personal assessments, biases, loyalties, and confidence rather than data collected from repeated trials. Their probability judgments come from their own perspectives, making this a classic example of subjective probability.
Option 3: Relative frequency probability. This approach relies on empirical data from past trials to estimate the likelihood of outcomes (e.g., the observed proportion of times a team won in the past). The question does not indicate any data collection or historical frequency being used; it emphasizes personal conviction, not empirical frequencies, so this is not what’s happening here.
Option 4: Classical probability. This method calculates probability from theoretical principles assuming equally likely outcomes (e.g., rolling a fair die). There is no assertion that outcomes are equally likely or that a formal model is used to derive equal chances; the friends’ bets reflect belief rather than a symmetric theoretical model, so this is not the best match.
In summary, the scenario hinges on a personal judgment about future sports results rather than empirical data or a formal symmetric model, which aligns with subjective probability. The other options describe more data-driven or assumption-based frameworks that do not capture the described situation.

OSC 2030-009 Fall 2025 SUBMIT: Graded Homework Module 3 (Chap 4)

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