Ask Dr. Math

High School Archive

Browse High School Probability
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Coin tossing.
    Odds vs. probability.
    Poker probabilities.
    Rolling dice.

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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?

M Balls in N Boxes [01/24/2002]

Suppose we put m balls into n boxes. What is the expected number of empty boxes?

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 variable?

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 variables?

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 just two?

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 answer...

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 VAriance) procedures?

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 the lottery...

Neighboring Cards [02/18/1997]

If you pick any two cards and then go look for them in the deck, what is the probability that you will find them next to each other?

Nickel Landed on Edge [10/11/2002]

What are the odds of throwing a coin and having it land on edge?

Normal Distribution [6/24/1996]

In six successive independent 'triple jumps' what is the probability that at least one total distance will exceed 18 meters?

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