See also the
Dr. Math FAQ:
probability in the
Browse High School Probability
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Odds vs. probability.
- Infinite Monkeys on Infinite Typewriters Producing Shakespeare [01/02/2006]
An interesting discussion of the classic monkey problem which focuses
on how we know that the works of Shakespeare will eventually be produced.
- Infinite Probability: A Point on a Line [11/03/2004]
Imagine a line extending infinitely in both directions. A line segment
of length 10m has endpoints at point A and point B, both of which are
on the line. What is the probability that a randomly chosen point on
the line falls on line segment AB?
- Infinite Series Problem [01/15/2002]
I have to find the correct answer to an infinite series question about
three people throwing dice...
- Intriguing Limit [04/30/1997]
Why is the following true: lim x --> oo (1-1/x)^x = 1/e?
- Johnny Carson's Birthday Problem [04/03/2002]
Carson picked people at random. Why didn't the probability work out?
- The Law of Large Numbers [02/08/2001]
Can you give me a brief explanation of the law of large numbers?
- Law of Large Numbers and the Gambler's Fallacy [05/07/2001]
Should you get the same total, on average, when you make three throws of
three dice each as when you throw nine dice at once? Also, can you
explain the Law of Large Numbers and the Gambler's Fallacy?
- Law of Random Numbers [12/22/1997]
I've recently been debating over the lottery...
- Let's Make a Deal Probability [06/01/1999]
In "Let's Make a Deal," does Monty's showing you a door, or his knowing
which door the prize is behind, affect the probability?
- Letters and Envelopes - the Inclusion-Exclusion Principle [03/27/1999]
What is the probability that no rabbit will escape into its own hole?
- Lifespan Probability [03/26/1999]
The probability that a general population will live past 85 is estimated
to be 5.4 percent...
- Line through a Disc, Terminating Zeros [12/03/1997]
1. A circular disc contains 2 billion randomly situated points. Can a
straight line pass through the disc and have exactly 1 billion points on
each side? 2. Find the terminating zeros in the standard numeral 580!
- Listing Sample Spaces [02/13/2003]
An urn contains 2 red, 2 black and 1 green ball, from which a sample
of two is chosen without replacement. Determine a sample space of
equally likely outcomes and assign probabilities.
- Lost Town and Finder's Town: Bayesian Probability [04/27/1999]
A man is lost in the mountains... what's the probability that he's
wandered into Lost Town? Finder's Town?
- Lottery Permutations [5/16/1996]
Determine the number of unique permutations of a lottery where you pick 6
numbers out of 49, and numbers may not repeat...
- Lottery Probability [01/23/1998]
Let's say that Monday's winning numbers were 1,2,3,4,5, and 6. Is the
probability that those winning numbers will come up again the same?
- Lottery Strategy and Odds of Winning [04/27/2000]
Are my odds of winning the lottery the same whether I choose the same
numbers each time or whether I choose different numbers?
- Lung Cancer and Smoking [10/20/2001]
Medical researchers know that the probability of getting lung cancer if a
person smokes is .34. The probability that a nonsmoker will get lung
cancer is .03. If 11% of the population smokes, what is the probability
that a person with lung cancer will have been a smoker?
- Making a Conditional Probability Chart [05/17/2000]
In a group of patients screened for lung cancer, 10% have the disease. Of
those who have lung cancer, 93% are smokers. Of those who do not have
lung cancer, 28% are smokers. If a person selected from this group is a
smoker, what is the probability that the person has lung cancer?
- Marbles and Dice [08/07/1997]
What is the probability that from three black and one red marble in a
jar, one red and one black marble will be picked without replacing the
marbles? Two ordinary dice are thrown. What is the probability that the
sum will be six or at least one of the two faces will be odd?
- A Markov Chain Example [07/01/1998]
We are given P pots with N balls each and take B balls out of them, where
B < N. On average, how many pots do we touch?
- Mathematical Card Trick [04/07/2002]
Take a deck of 52 cards. Shuffle; flip over the top card and count
from that number to King. Do this until you can no longer count to a
King. Excess cards become 'dead cards.'
- Math in Card Games [10/06/2000]
How is math involved in creating and playing card games?
- Mean and Standard Deviation [03/01/1999]
Prove that the mean (u) and standard deviation (s) for a binomial
distribution are np and the square root of (npq).
- Measuring the Randomness of a Shuffled Deck [12/19/2003]
I'd like to compare how well humans and computer programs can shuffle
a deck of cards, but I need some way to measure the randomness of a
shuffle. How can I do this?
- Moment-generating Function of a Binomial Random Variable [10/27/1999]
How can I find the moment-generating function (MGF) of a binomial random
- Moment Generating Functions [06/20/1998]
Can you help me with the following proofs on moment generating functions?
- Moment Generating Functions [03/30/1999]
What can be established about the sum of negative binomial random
- Monkeys Typing Shakespeare: Infinity Theory [08/05/1998]
Would an infinite number of monkeys typing at random eventually produce
the entire works of Shakespeare?
- Monte Carlo Method and Computer Simulation [04/04/2002]
What is the Monte Carlo method? I know it's for estimating
probability, but what is the point of it?
- Monty Hall Logic [03/09/2001]
Are there in fact four options? Aren't there three choice points, not
- Monty Hall Strikes Again [11/2/1994]
There are three cups, one of which is covering a coin. I know the
whereabouts of the coin, but you don't. You pick a cup, and I take one of
the remaining cups, one which DOESN'T contain a coin. Both you and I know
the cup I pick doesn't contain a coin. You then have the option to swap
your cup with the third, remaining cup, or keep your first choice. What
is the probability of the coin being in the cup if you keep your first
choice, or if you decide to swap them?
- More Living or Dead? [08/14/1997]
Are there more people living now than have ever died?
- Most Desirable Properties in Monopoly [02/16/2001]
What are the most desirable properties on a Monopoly board? How can we
calculate the overall probability of landing on a given property?
- Most Frequently Rolled Number [10/27/1999]
What sum would be rolled most often if two dice, each numbered -3, -2, -
1, 0, 1 and 2, were rolled 100 times?
- Multiple Choice Test: Binomial Probability [08/05/1997]
A multiple choice test consists of 9 questions with 5 choices for each
- Multiple Choice Tests [05/06/1997]
If you have a test with 6 questions and 4 possible answers to each
question and you guess all answers, what is the probability of getting
all 6 questions right?
- Multiple Regression vs. ANOVA [09/20/1999]
What is the difference between multiple regression and ANOVA (ANalysis Of
- Murder Rate Probability [01/12/1998]
If a Midwestern town has a murder rate of 11 murders per year, what are
the chances that 3 of them will occur on the same day?
- NCAA Lottery Formula [08/27/1997]
I have forgotten the formula for this probabilities/odds question about