mgmt650 week 3 discussion latest 2016 september

Week 3

Discussion: Probability Paradox

A family member can go to one of two local hospitals for heart surgery.

Checking the history for the past year, you find that each of the two hospitals has performed cardiac surgery on 1000 patients. In hospital A 710 patients survived (71%). In hospital B 540 (54%) survived.

Based on the numbers presented, which hospital do you think is superior in cardiac surgery?

Surely hospital A is better, right?

Now, let’s look at more data. The below chart summarizes three categories of patients (those entering in fair, serious and critical condition) and the survival rate from surgery (in percent) for the two local hospitals.

Patient Entering Condition

Hospital A

Hospital B

Survivors from A (# and percent)

Survivors from B (# and percent)

Fair

700

100

600 or 86%

90 or 90%

Serious

200

200

100 or 50%

150 or 75%

Critical

100

700

10 or 10%

300 or 43%

Total

1000

1000

710 or 71%

540 or 54%

Looking at the data broken down in this way, we see that Hospital B has a higher success rate in all three categories of patients but when averaged all together, Hospital A has the higher overall survival rate. Based on the numbers presented, which hospital do you think is superior in cardiac surgery?

Probability Puzzles

Please select one below to work on and share your answer.

Probability Puzzle 1: The Birthday Problem

There are 23 people in this class. What is the probability that at least 2 of the people in the class share the same birthday?

Probability Puzzle 2: The Game Show Paradox

Let’s say you are a contestant on a game show. The host of the show presents you with a choice of three doors, which we will call doors 1, 2, and 3. You do not know what is behind each door, but you do know that behind two of the doors are beat up 1987 Hyundai Excels, and behind one of the doors is a brand new Cadillac Escalade. The cars were placed randomly behind the doors before the show, and the host knows which car is where. The way the game is played out is as follows. The host lets you choose a door. Assume you choose door #1. Before he opens door #1 to let you see what you have chosen, he opens one of the remaining doors, say door #3, to reveal a Hyundai Excel (he will always open one of the remaining doors that has the booby prize), and asks you whether or not you want to change your choice to door #2. What do you tell him?

Probability Puzzle 3: Flipping Coins

If you flip a coin 3 times, the probability of getting the sequence HTH is identical to the probability of getting HTT (1/8). Let’s make this situation a little more interesting. Suppose you are going to flip a coin until you get the sequence HTH. Say this takes you x flips. Then, suppose you are going to flip the coin until you get the sequence HTT. Say this takes you z flips. On average, how will x compare to z? Will it be bigger, smaller, or equal?

Probability Puzzle 4: Disease Testing and False Positives

Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease?

Probability Puzzle 5: A girl named Florida

Here's a three part puzzler:

1. Your friend has two children. What is the probability that both are girls?

2. Your friend has two children. You know for a fact that at least one of them is a girl. What is the probability that the other one is a girl?

3. Your friend has two children. One is a girl named Florida. What is the probability that the other child is a girl?

The Value of Variance

More often than not, when we are presented with statistics we are given only a measure of central tendency (such as a mean). However, lots of useful information can be gleaned about a dataset if we examine the variance, skew, and the kurtosis of the data as well. Choose a statistic that recently came across your desk where you were just given a mean. If you can't think of one, come up with an example you might encounter in your life. How would knowing the variance, the skew, and/or the kurtosis of the data give you a better idea of the data? What could you do with that information?

Example: Say you are an executive in an automobile manufacturer, and you are told that, for a particular model of new car that you sell, buyers have on average 2.2 warrantee claims over the first three years of owning the car. What would additional information on the shape of your data tell you? If the variance was low, you’d know that just about every car had 2 or 3 warrantee claims, while if it was high you’d know that you have a lot of cars with no warrantee claims and a lot with more than 2.2. The skew would provide similar information; with a high level of right skew, you’d know that the average is being brought up by a few lemons; with left skew you’d know that very few of the cars have no warrantee claims. The kurtosis (thickness of the tails) would help you get an idea as to just how prevalent the lemon problem is. If you have high kurtosis, it means you have a whole bunch of lemons and a whole bunch of perfect cars. If you have low kurtosis, it means that you have few lemons but few perfect cars.