1. In class, we have discussed the interpretation of probability as a relative f

Question

1. In class, we have discussed the interpretation of probability as a relative frequency ("objective"). Another interpretation of probability is as a measure of belief about the likelihood an event will occur in a particular replication ("subjective"). Suppose you ask a friend about the chance of rain tomorrow. Not having had this class, your friend replies with the belief that there is ·a 30% chance of rain today, a 40% chance of rain tomorrow. a 20% chance of rain both today and tomorrow, and a 60% chance of rain either today or tomorrow Are these subjective probabilities consistent with the axioms of probability? Why or why not? If not, propose new subjective beliefs that are consistent with the axioms of probabilit;y

Explanation / Answer

Let Event A: Rain today => P(A) = 0.30
Let Event B: Rain Tomorrow => P(B) = 0..40
Chance of rain both today and tomorrow, i.e. P(A B)
Since events A and B are independent: P(A B) = P(A) . P(B) = 0.30 x 0.40 P(A B) = 0.12
Chance of rain either today or tomorrow, i.e. P(A U B)
Using axiom: P(A U B) = P(A) + P(B) - P(A B)
P(A U B) = 0.30 + 0.40 - 0.12 = 0.58
Hence the subjective probabilities given are not consistent with the axioms of probability. New subjective beliefs are:

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.