Discuss the following statement. \'The probability of event E is considered \"su

Question

Discuss the following statement. 'The probability of event E is considered "subjective" if two rational persons A and B can assign unequal probabilities to E, PR_A(E) and Pr_B(E) These probabilities can also be interpreted as "conditional": PR_A(E) = PR(E/I_A) and PrB(E)= PR(E/I_B), where I_A and I_B represent the knowledge available to persons A and B, respectively. Apply this idea to the following examples: The probability that a '6' appears when a fair die is rolled, where A observes the outcome of the die roll and B does not. The probability that Brazil wins the next World Cup, where A is ignorant of soccer and B is a knowledgeable sports fan.

Explanation / Answer

a)

For example, A saw that the die result was 4. Then, A may think that the next outcome is most probably a 4 as well. However, B may think that each outcome must have the same probability.

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b)

If A is ignorant at soccer, then he might think that all teams have the same chance at winning. But for B, a knowledgeable sports fan, he know the history of the Brazilian team at the World Cup, their current roster, etc., so he may assign a different probability than just an equal chance for all the teams.

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