Register to reply

Help with Probability question.

by Kiziaru
Tags: probability
Share this thread:
Feb17-12, 10:52 AM
P: 6
So I've been trying to do probability problems to take the P/1 Exam, and I've come across a problem that I don't quite understand.


An insurance company estimates that 40% of policyholders who have only an auto policy
will renew next year and 60% of policyholders who have only a homeowners policy will
renew next year. The company estimates that 80% of policyholders who have both an
auto and a homeowners policy will renew at least one of those policies next year.
Company records show that 65% of policyholders have an auto policy, 50% of
policyholders have a homeowners policy, and 15% of policyholders have both an auto
and a homeowners policy. Using the company’s estimates, calculate the percentage of
policyholders that will renew at least one policy next year.

Attempt at solution:

Pr(A ∩ H(compliment)) = Pr(A - H) = Pr(A) - Pr(H)

Pr(A) = .65
Pr(H) = .50

.65 - .50 = .15

However, the solution claims that Pr(A - H) = Pr(A-(A ∩ H)) = .50. How is that possible? How did they derive that?

Edit: Disregard, I understand it now. I had to apply the Pr(A U B) = Pr(A) + Pr(B) - Pr(A ∩ B) rule.
Phys.Org News Partner Science news on
Climate change increases risk of crop slowdown in next 20 years
Researcher part of team studying ways to better predict intensity of hurricanes
New molecule puts scientists a step closer to understanding hydrogen storage

Register to reply

Related Discussions
Probability question; Conditional probability and poisson distribution Precalculus Mathematics Homework 1
Probability Question About The Poisson Probability Distribution Calculus & Beyond Homework 15
[probability theory] simple question about conditional probability Precalculus Mathematics Homework 1
Hard probability question (cambridge exam question) Set Theory, Logic, Probability, Statistics 3
Series Question (from a probability question) Calculus & Beyond Homework 3