# Question

Subjective probabilities may be determined by exposing persons to risk- taking situations And finding the odds at which they would consider it fair to bet on the outcome. The odds are then converted into probabilities by means of the formula of Exercise 2.15. For instance, if a person feels that 3 to 2 are fair odds that a business venture will succeed (or that it would be fair to bet $ 30 against $ 20 that it will succeed) , the probability is 3 / 3 + 2 = 0.6 that the business venture will succeed. Show that if subjective probabilities are determined in this way, they satisfy

(a) Postulate 1 on page 28;

(b) Postulate 2.

(a) Postulate 1 on page 28;

(b) Postulate 2.

## Answer to relevant Questions

Show that the postulates of probability are satisfied by conditional probabilities. In other words, show that if P(B) ≠ 0, then (a) P(A| B) ≥ 0; (b) P(B| B) = 1; (c) P(A1 ∪ A2 .. ∪ . | B) = P(A1| B) + P(A2| B) + · ...Show that if events A And B are independent, then (a) Events A' And B are independent; (b) Events A' And B' are independent. Prove Theorem 2.12 by making use of the following generalization of the distributive law given in part (b) of Exercise 2.1: A ∩(B1. B2. · · · ∪ Bk) =(A ∩ B1) .(A ∩ B2) ∪ · · · ∪ (A ∩ Bk) A coin is tossed once. Then, if it comes up heads, a die is thrown once; if the coin comes up tails, it is tossed twice more. Using the notation in which (H, 2) , for example, denotes the event that the coin comes up heads ...In a group of 200 college students, 138 are enrolled in a course in psychology, 115 are enrolled in a course in sociology, And 91 are enrolled in both. How many of these students are not enrolled in either course?Post your question

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