Conditional Proabilities
TIA focused quite a bit of attention on tables in discrete probability but there weren't any tables used in conditional.
I believe using tables is going to be the fastest way for me to solve a problem with confidence, so I decided to construct a table to see how it would be used.
This actually makes it simple. No matter what kind of question you get you'll be able to fill in the blanks and solve the problem. In lesson two, I noticed all the problems had a least one column where the total space equaled 1. This space is the total probability space. The next column was a condition, and I noticed that these didn't add up to 1. (in this problem it adds up to .1, but that is a coincidence)
using the formulas you're going to attempt to get to sum of the products of whatever categories you are using. To do this, you just add a column called product, do the multiplication, and get the sum.
Now the problem asks, "Calculate the probability that the driver was 1620"
Well, you know the total probabilty of occurance is going to be .0303 and that 1620 year olds are responsible for .0048 of that, or 15.84%
This image gives you a more visual look at what is happening, but I find it's harder to get to the answer if you make it look this way.
I imagine this method will work for all the problems, I'll let you know if I come across any flaws in it as I finish the problem set given by TIA
here is how the tables work on another problem:
An insurance company issues life insurance policies in three seperate categories: standard, preferred and ultrapreferred. Of the company's policyholders, 50% are standard, 40% are preferred, and 10% are ultra preferred. Each standard policyholder has a probability of 0.010 of dying in the next year, each preferred policyholder has probability 0.0050 of dying in the next year, and each ultrapreferred policyholder has probability 0.001 of dying in the next year.
A policyholder dies in the next year.
What is the probability that the deceased policyholder was ultrapreferred?
I believe using tables is going to be the fastest way for me to solve a problem with confidence, so I decided to construct a table to see how it would be used.
This actually makes it simple. No matter what kind of question you get you'll be able to fill in the blanks and solve the problem. In lesson two, I noticed all the problems had a least one column where the total space equaled 1. This space is the total probability space. The next column was a condition, and I noticed that these didn't add up to 1. (in this problem it adds up to .1, but that is a coincidence)
using the formulas you're going to attempt to get to sum of the products of whatever categories you are using. To do this, you just add a column called product, do the multiplication, and get the sum.
Now the problem asks, "Calculate the probability that the driver was 1620"
Well, you know the total probabilty of occurance is going to be .0303 and that 1620 year olds are responsible for .0048 of that, or 15.84%
This image gives you a more visual look at what is happening, but I find it's harder to get to the answer if you make it look this way.
I imagine this method will work for all the problems, I'll let you know if I come across any flaws in it as I finish the problem set given by TIA
here is how the tables work on another problem:
An insurance company issues life insurance policies in three seperate categories: standard, preferred and ultrapreferred. Of the company's policyholders, 50% are standard, 40% are preferred, and 10% are ultra preferred. Each standard policyholder has a probability of 0.010 of dying in the next year, each preferred policyholder has probability 0.0050 of dying in the next year, and each ultrapreferred policyholder has probability 0.001 of dying in the next year.
A policyholder dies in the next year.
What is the probability that the deceased policyholder was ultrapreferred?
Total Comments 1
Comments

By the way, tables like that come in real handy when you do Bayesian credibility in exam 4/C with discrete priors. (Basically, just doing conditional probability on classes, as you're doing here, but then taking it another step to calculate expected number of losses the next year given the experience seen.)
Posted 01272009 at 09:29 AM by campbell