Solution Found!
In any given year, a male automobile policyholder will
Chapter 3, Problem 46P(choose chapter or problem)
Problem 46P
In any given year, a male automobile policyholder will make a claim with probability pm und a female policyholder will make a claim with probability pf, where pf ≠ pm. The fraction of the policyholders that are male is α, 0<α<1. A policyholder is randomly chosen. If Ai denotes the event that this policyholder will make a claim in year i, show that
P(A2|A1) > P(A1)
Give an intuitive explanation of why the preceding inequality is true.
Questions & Answers
QUESTION:
Problem 46P
In any given year, a male automobile policyholder will make a claim with probability pm und a female policyholder will make a claim with probability pf, where pf ≠ pm. The fraction of the policyholders that are male is α, 0<α<1. A policyholder is randomly chosen. If Ai denotes the event that this policyholder will make a claim in year i, show that
P(A2|A1) > P(A1)
Give an intuitive explanation of why the preceding inequality is true.
ANSWER:
Step 1 of 2
A male automobile policyholder will make a claim with probability pm und a female policyholder will make a claim with probability pf, where pfpm.
The fraction of the policyholders that are male is , 0<
1.
If denotes the event that this policyholder will make a claim in the year i.
We have to show that P(/
)= P(
).