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": PrA(E) = Pr (E|Ia) and P_r b(E) = P_r(E|Ib), 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. When a fair die is rolled, the outcome is independent of the observers. The probability of getting 6 remains 1/6 whether A and B observes or not. Therefore, PrA(E)=1/6 and PrB(E)=1/6.

b. Since A is ignorant of soccer, he has no knowledge of soccer. B has a good knowledge as he is a knowledgeable fan. Hence Pr(E|IB) would be closer to the actual chance of Brazil winning the World Cup.

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