Ask Marilyn.Answer two questions: First, how would you answer the reader's question. Then, how can anything be truly random?
Parade Magazine, 29 Oct. 1995, p. 18
Marilyn vos Savant
A reader writes:
From what I understand, computers do exactly what you instruct them to do. If so, how can a computer generate random numbers? How does someone write one set of instructions that would produce a different answer every time? It seems like an impossible task.Marilyn answers:
Michael H.G. Ho,
Sagamore Hills, Ohio
Computer programs don't generate numbers randomly, but the results can be used as random numbers. That's because they're likely to be "more random" than any other random number generator you can name, such as a deck of cards, or the fellow at the desk next to yours. After all, how can anything be truly random?
You may want to address these questions:
- What, in your own words, is the prosecutor's fallacy?
- The article provides an explanation of the prosecutor's fallacy. If you were a prosecutor, and the defense used such an explanation, how might you respond?
- How would you interpret the statement "'the defendant has the same DNA profile as that left at the crime scene by the perpetrator, and this type is estimated to occur in one in a million people" in the context of a criminal trial?
- Some people have criticized prosecutors who quote extremely small probabilities for matching the defendent to the DNA at the crimescene. For example, if I say that the probability that such a match occurred by chance alone is 1 in 6 billion, what does this mean, given that there are only 5 billion people in the world? What do you think this means? Does this bother you? Why or why not?
- Can you think of any other examples of probabilities that are often misunderstood by the public?
- What probability concepts have you found to be counterintuitive?
Instructions on how to write an essay.
Before continuing, read the following story from the Boston Globe.
The headline says it all: BU analysis says Washington march may have drawn 1.1 million.
Now, address these questions:
- If you are using photographs for the headcount, what factors need to be controlled to get an accurate count? Where should you take these pictures, at what time of day? If you wanted to influence the count, how would you do it?
- The error term in BU's analysis was a "resolution" error. Can you explain how they might have arrived at this (or any) error rate?
- What methods, other than aerial photography, might be used to help corroborate the numbers?
- Are there are any advantages/disadvantages to using a video tape instead of a still photo?
- How would you count the crowd?
- Do you think we will ever know how many were in attendance?
This is pretty heated stuff, and you have probably already formed an opinion. While your opinion is valuable, and can certainly be included in your essay and any other discussion, the assignment is to analyze some of D'Souza's reasoning. (This is quoted from Forbes, so it's possible they got it wrong.) From pg. 60 of the magazine:
In the case of the risk for banks in mortgage lending, the government's answer [to the question: should governments force (banks) to take a risk to defuse racism] seems to be: yes. D'Souza chronicles many recent news stories about differeing loan rejection rates between blacks and whites. These have provided the Clinton Administration with an excuse to force banks to increase their minority lending.First, note that alot of the argument hangs on the word "unfairly" in that last paragraph. But of interest to a statistician is the model proposed here. The world consists of two kinds of borrowers: the good, and the defaulters. A bank sees a random sample, and has to decide which they are. By reviewing past evidence, we can see how successful they've been. Banks have been rejecting black borrowers at a greater rate than they have for white borrowers, and under this policy the default race for both categories is the same. D'Souza wants us to take this as proof that the banks are doing the right thing. But there is (at least from a statistics/probability) point of view, a flaw in his reasoning. What is it?Citing Forbes (jan. 4, 1994), D'Souza says the best evidence suggests that black and white default rates are about the same. If the banks had been rejecting black applicants unfairly, the black default rate would be lower. So the banks' credit judgements were accurate after all.
What do you think of his reasoning? Why?
Instructions on how to write an essay.
"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?"What do you think? Why? What assumptions are you making? (Hint: you should probably assume that the host knows where the car is.)
This problem caused quite a controversy when Ms. Vos Savant published her answer. You might want to look into this when you write your essay. It's rather unintuitive, and some people refuse to believe in the answer. What did your classmates think? What kind of intuition was used, and what arguments were convincing?
Think about your answer, and then try posting it to the Chatroom for some input. Or maybe you can read what others have said there and help them, or criticize/support their arguments.
Instructions on how to write an essay.
