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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.



Probability of Forming a Triangle [08/09/1999]
Three numbers are chosen (without picking the same number twice) from the first n natural numbers. What is the probability that they can be the three sides of a triangle?

Probability of Getting a Job [7/10/1996]
If there are 5 different jobs, and a person has a ten percent chance of getting any one job, what is the chance of getting any job at all?

The Probability of Getting Dealt 4-of-a-kind [3/21/1995]
What is the probablitiy of being dealt 5 cards and getting four of a kind?

Probability of Getting your Hat Back [12/9/1995]
There are 5 people with 5 hats. The hats are put into a box. What is the probability that each person will get his or her hat?

Probability of Having a Girl after Five Straight Boys [04/19/2005]
In a family with 5 children, ALL of whom are boys, what is the mathematical probability that the 6th child will be a girl?

Probability of Independent Events [02/07/1997]
If the probability of an event is known, is there a formula that will gives the probability of that event after a given number of trials?

Probability of Infection [03/06/1998]
How many of six hermits can be expected, on average, to get a disease, assuming the disease is transmitted until an infectious hermit visits an immune hermit, and assuming one hermit visit per day?

Probability of Making Triangle with Three Stick Pieces [02/24/2007]
Take a stick of unit length and break it into two pieces, choosing the break point at random. Now break the longer of the two pieces at a random point. What is the probability that the three pieces can be used to form a triangle?

Probability of Matching Envelopes and Letters [03/03/1998]
Using inclusion-exclusion to calculate probability of matching no, then exactly one, letter with its envelope.

Probability of Matching Times on a Clock [09/14/2004]
What is the probability of two different times within the same hour ending in the same last digit, such as 8:13 and 8:43?

Probability of Never Having a Losing Record [04/07/2001]
Suppose a football team plays 8 games, and the chance of winning any particular game is 50%. What is the probability of completing the season without more losses than wins?

The Probability of Outcomes [2/20/1995]
In the sample space for a probability experiment, outcome A is twice as likely as outcome B. Outcome C is two-thirds as likely as outcome B. Outcome C is twice as likely as outcome D. Find the probability of each outcome in the sample space.

Probability of Picking Coins [01/12/2003]
Max has 5 coins in his pocket that total 47 cents. What is the probability that he will reach into his pocket and pull out a dime, and then without replacing it reach in and pull out a quarter?

Probability of Picking in the Correct Order [4/12/1996]
Out of a population of 200 different amino acids, what is the probability of selecting the correct 20 acids in the correct order on your first try.

Probability of Random Samples by Complementarity, Inclusion, and Exclusion [08/09/2012]
Given a set S = {A_1, A_2, A_3, ..., A_N}, a probability student struggles to enumerate all cases of random samples of size k that contain at least its first two elements, A_1 and A_2. Doctor Schwa provides hints based on complementary probability and the principle of inclusion and exclusion.

Probability of Rolling 2 At Least Twice [7/3/1996]
A fair die is rolled three times. Find the probability of rolling a "two" at least twice.

Probability of Success with Random Guessing [07/10/2008]
I read that if 25 students take a 10-question true or false test and they all randomly guess at the answers, there is a 75% chance that at least one of them will score 80% or better. How is that possible? It seems too high to me.

Probability of the Same Birthday within a Group [8/22/1995]
What is the probability that, in a room of 30 people, two people will have the same birthday?

Probability of Void Hand in Card Game of Bridge [12/02/2004]
What is the probability of being dealt a bridge hand void in a specified suit from an ordinary deck of 52 playing cards?

Probability of Winning a Solitaire Game [10/26/1995]
I am interested in finding out how to figure the probability of winning the solitaire 'clock game'.

Probability of Winning in Squash [06/23/1999]
In a game of squash tied at 8 all, determine whether the player receiving the serve has a better chance of winning if she calls 9 or 10 points.

Probability of Winning Roulette [5/16/1996]
How can we calculate, discuss, and demonstrate the probabilities and mathematical expectations of roulette?

Probability: Permutations and Combinations [12/10/2002]
How is probability related to permutations and combinations?

Probability Philosophy and Applying Inference [10/11/2004]
If I flip a coin 4 times and they all turn out to be heads, what is the probability that the coin is fair?

Probability Problem in a Lewis Carroll Book [12/13/2008]
Say that 70 percent of a group of soldiers have lost an eye, 75 percent an ear, 80 percent an arm, and 85 percent a leg. What minimum percentage must have lost all four?

Probability Question from a Math Test [3/8/1996]
There are 15 homerooms in the school and 20 students in each homeroom. If the principal selects 5 of the homerooms for a pizza party, what is the probability of Mr. Smith's homeroom being selected?

Probability that 6 Peas will Sink [1/23/1996]
We need to know the probability that all six of these durn peas will be floating on top of the water before they are all six sunk down to the bottom of the jug...

Probability That a Function Has Real Roots [9/24/1995]
If r and s are numbers between 0 and 9, inclusive, what is the probability, P, that the function f(x) = x2 +rx + s has real roots? This question will consider only the case where r and s are integers.

Probability that a Random Integer... [7/18/1996]
How do I figure out the the probability that an integer chosen randomly would be an integer multiple of a given integer "n" ... or the probability that it would be a multiple of 2...7, and so on...?

Probability That a Sum Is Divisible by Three [11/04/2009]
How many ways can you choose three numbers from 1-100 whose sum is divisible by three?

Probability That Random Chord Exceeds Radius in a Circle [11/20/2004]
If a chord is selected at random on a fixed circle, what is the probability that its length exceeds the radius of the circle?

Probability That Someone Shares Your Birthday [05/14/2002]
How many people would you have to share a room with before the probability that one of them shares your birthday is at least 50%?

Probability Theory: Coincidental Birthday [06/21/1998]
In more than half the classes in a school, there are at least two children with the same birth date...

Probability Transition Matrices [02/10/1999]
How do you use probability transition matrices to find probabilities after the first transition?

Probability Tree Diagrams [8/22/1996]
What are the odds that two children will both be boys, firing once will hit a target, cargoes will arrive ruined?

Probability Trees [07/26/1998]
A bottle cap machine packs a defective cap in one box in ten. What is the probability the next four boxes will have a defective bottle cap?

Probability vs. Odds, Explained [03/21/2002]
Given a coin with heads on one side and tails on the other, what are the odds in favor of getting heads, and the odds against?

Probability with the Poisson Distribution [10/16/1998]
Can you help me find a probability using a Poisson distribution? I need to be able to manipulate lambda.

The Probable Pen in the Cereal Box [11/25/1999]
Six different-colored pens are offered as prizes in boxes of breakfast cereal. How many boxes of cereal do you have to buy to get all six?

Prove Sum nci = 2^n ... [05/30/1998]
I would like to know how to prove sum nci = 2^n with 0<=i<=n.

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