Bayes' Theorem

[sillyarms]

I'm having some trouble in one of my classes. I do not understand bayes theorem and have a teacher who refuses to take the time to explain it to me. However I really need to know it. Here is a problem from the book. This is not a problem given homework assignment, however it is similar to the problem in the homework assignment.

Sport utility vehicles(SUVs), vans, and pickups are generally considered to be more prone to roll over than cars. In 1997 24.0% of all highway fatalities involved a rollover; 15.8% of all fatalities in 1997 involved SUVs, vans, and pickups, given that the fatality involved a rollover. Given that a rollover was not involved, 5.6% of all fatalities involved SUVs, vans, and pickups. Consider the following definitions:

A = fatality involved an SUV, van, or pickup
B = fatality involved a rollover

a. Use Bayes' theorem to find the probability that the fatality involved a rollover, given that the fatility involved an SUV, van, or pickup.

Here is what I got(although I don't beleive it is correct).

A = .158 + .056 = .214
B = .24

P(B|A)= [P(A|B)P(B)]/P(A)
= (.158*.24)/.214
= 0.17719626168224299065420560747664

if anyone could help me out by showing me the error of my ways it would be greatly appreciated.

thanks

silly

[Siegmund]

The problem is with your calculation of P(A).

You are given P(A|B)=.158 and P(A|~B)=.056.

But P(A) is not P(A|B)+P(A|~B), it is P(A and B)+P(A and ~B)
, which you can calculate as P(A|B)P(B) + P(A|~B)P(~B).