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.
- Random Card Shuffling Probabilities [6/11/1996]
What is the probability of at least two eights being next to each other
in a random shuffling of a deck of cards. What about at least two cards
(2 eights or 2 queens etc.) being next to each other?
- Randomly Cutting a Rope into Two Segments [05/14/1998]
A rope 20m long is randomly cut into two segments, each of which is used
to form the perimeter of a square . . .
- Randomly Selecting a Card [02/20/1998]
What is the probability that a card randomly selected from a standard
deck will be a king and a club?
- Randomly Setting the Table [01/25/1999]
Using tree diagrams or incremental analysis to calculate the probability
that, out of four differently colored and randomly placed settings, at
least one setting (cup, saucer, and plate) is of the same color.
- Returning Homework and Probability [12/11/1998]
When homework assignments are handed back at random, what is the
probability that a student will receive his or her own paper?
- Riemann, Mayan Math [5/20/1996]
Math projects: A. Riemann - a German mathmatician; B. The Mayan number
system and calendar; C. Probability.
- Rolling 3 Pairs with 6 Dice [12/19/2001]
Upon playing the game '10,000' on the computer I was struck by the
frequency with which 3 pairs came up...
- Rolling a Die 600 and 5000 Times [06/03/2001]
Toss a die 600 times, 5000 times. How many times does each number come
up? Approximately how many would you expect?
- Rolling One Die Twice [03/25/2002]
If one die is rolled twice, what is the probability of getting a 10?
- Roulette Betting "System" [08/07/1997]
One roulette system is to bet $1 on black. If black comes up on the first
spin of the wheel, you win $1 and the game is over...
- Roulette Probability [12/07/1997]
What is the probability of winning a certain amount of money using only
the even money bets and the two to one bets?
- Roulette Questions [01/26/1998]
What is a safer bet: to bet on a number, or to bet on color? Which bet
maximizes your wins: betting on numbers, or betting on colors?
- Running Shoes [02/07/2001]
What proportion of the time does the runner run barefoot?
- Sample Space Diagram [07/30/1999]
If a person randomly chosen from a population is found to be colorblind,
what is the probability that the person is male?
- Satellites and Dartboards [02/21/2000]
If I know the surface area and number of satellites in orbit, and the
divergence of a laser beam fired from a random point on earth, how can I
determine the probability of hitting one of the satellites?
- SAT Probability Problems [11/12/1996]
What is the best way to solve probability problems on the SAT?
- Selecting a Student Council [10/08/1997]
What is the probability of a student being selected in each of the
- Sequence of Letters [04/23/1999]
Given an alphabet of 10 letters and a sequence of 600 letters, what is
the probability of finding the subsequence DDDD?
- Server Traffic [01/02/1999]
Can you help me find a Poisson probabilistic model for number of arrivals
per minute, length of connection, etc. ...?
- Several Probability and Statistics Techniques [04/13/1998]
Examples of binomial distribution, Poisson distribution, significance
test, and calculation of confidence interval.
- Sharing a Zodiac Sign [04/24/2001]
In a class of 35 students, what is the probability that every student in
the class will have the same zodiac sign as at least one other classmate?
- Should You Play? [08/07/1997]
A game consists of three cuts with a deck of 52 cards. You win $1 if a
face card turns up on at least one cut, but you lose $1 if one does not
turn up. Should you play?
- Similar Phone Numbers [10/21/1996]
What is the probability that two telephone numbers will contain the same
numbers but in a different order?
- Simplifying a Probability Question [08/19/2008]
An example of how a probability question that seems difficult or
confusing can often be simplified by translating it into an equivalent
situation involving colored balls in a jar.
- Slot Machines [5/29/1996]
What are the probabilities and mathematical expectations of slot
- Social Security Number Probability [02/09/2004]
What are the chances that a 9-digit Social Security number is
comprised entirely of 2 digits, such as 211-12-1221?
- Space Diagrams [02/28/2002]
A bag contains 3 blue balls, 1 red ball and 1 white ball. A second bag
contains 1 blue ball and 4 red balls. A ball is chosen at random from
each bag. Draw a sample space diagram to show the possible outcomes.
- Squares Having a Common Side [03/08/1999]
What is the probability that two squares of a chessboard will have a
- Standard Deviation and Conditional Probability [07/14/1998]
If a sample has one element, what is its standard deviation? Also, can
you help me with a conditional probability problem?
- Stochastic Matrices [03/17/1998]
Finding the transtion matrix and steady-state vector of a stochastic
- Stock Market Scam [02/08/2001]
Every Monday a firm sends you a letter correctly predicting the behavior
of a given stock over the coming week. In the 8th letter the firm offers
to sell you more predictions for a fee. You refuse. Why?
- Stocks and the Binomial Distribution [12/09/1998]
If an index of stock prices has probability 0.65 of increasing in any
year, how can you turn this into a binomial distribution question?
- Stolen Base [08/29/1997]
I need to create a mathematical model for a stolen base...
- Strategy and Expected Value of Dice Game [09/03/2005]
After rolling a die, you can collect the amount that shows on the face
of the die, or you can reject that payoff and roll again. You collect
only the amount of the most recent roll, and you may choose to roll up
to three times. What is the expected payoff of this game?
- Sum of 5 or 7: Dice Probability [09/11/2002]
A pair of dice is rolled until a sum of either 5 or 7 appears. Find
the probability that a 5 will occur first.
- Sum of Two Arcs [01/30/2003]
Three points are taken at random on the circumference of a circle.
What is the chance that the sum of any two arcs so determined is
greater than the third?
- Sum of Two Dice [12/05/2001]
Find the probabilities of rolling different sums.
- Survey Respondents Flip Coins [08/04/1997]
Survey respondents are asked to flip a coin in private and answer
question A if the result is a head and question B if the result is a
tail... what's the probability that Question A will be answered "Yes"?
- Ten Coin Flips, Four Heads [05/08/2001]
If you flip a coin ten times, what is the probability of getting at least
- Ten Ducks and Ten Hunters [02/03/2000]
Ten ducks fly overhead. Each of ten hunters picks one duck at random to
aim at and kill it with probability P. What is the mean number of ducks