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.
- Probabilities and Expected Value in Seating Arrangements [05/12/1998]
Three couples are seated at random around a round table. Let M denote the
number of husbands seated next to their wives ...
- Probabilities in a Dice Game Using Markov Analysis [03/22/2004]
Anne, Bob, and Carmel are going to take turns rolling a fair die, in
the order Anne, Bob, Carmel, Anne, Bob Carmel, etc. The first person
to roll a 6 will win $100.
a) Find the probability that Anne will win $100 if the first four
numbers rolled are 3, 2, 5, 5.
b) Find the probability that Anne will win $100 if a draw is to be
declared with nobody winning $100 in the event of a 6 not being
rolled within the first 8 rolls in total.
c) Suppose that a draw is to be declared if ever two 1's are rolled
in a row (by two different players). Also suppose that the game is
in fact over and did not end in a draw. Find the probability that
Anne is the player who won $100.
- Probabilities when Rolling 10 Dice [07/29/1999]
What are the odds of a player rolling the same numbers in the same order
as the house on 10 dice? ...of rolling the same numbers without regard to
the order in which they were rolled?
- Probability: 8-sided die [4/25/1996]
I have an octahedron - what's the probability I'll roll a seven?
- Probability and Odds [01/05/2008]
What is the difference between giving the probability that something
will happen and the odds that it will happen?
- Probability and Pascal's Triangle [06/04/1998]
How do I find the probability of getting 3 head and 2 tails using
- Probability and Ten-Sided Dice [06/23/2008]
What is the probability of a total roll greater than 95 when rolling
ten 10-sided dice with faces numbered from 1 to 10?
- Probability and the game of RISK [04/21/2000]
In the game of Risk the attacker rolls 3 dice, the defender rolls 2 dice
and high dice are compared...
- Probability and the Prisoner Problem [07/04/2001]
Each of 16 prisoners receives a hat that is either red or blue (the
colour is selected randomly; each has a 1/2 probability). All the
prisoners must simultaneously either try to guess the colour of their
hats, or pass.
- Probability and the 'Ways Method' [10/25/2002]
Suppose we roll one six-sided die. What are the possible outcomes?
What is the probabiliy of rolling a 4? If we have two dice how many
outcomes are there? With two dice what is the probability of rolling a
- Probability and Tossing a Coin [10/25/2004]
How would I calculate the probability of a tossed coin coming up heads
two times in a row before it comes up tails a total of ten times?
- Probability Axioms and Theorems [04/10/2001]
What are the laws of probability?
- Probability C Hits the Target First [09/08/2001]
A, B, and C keep shooting in the sequence: A,B,C,A,B,C... until a target
is hit. A hits the target 5/6 of the time, B 3/4 of the time, and C 2/3
of the time. What's the probability that C will hit the target first?
- Probability Distribution [12/22/1997]
A county with a large number of rural homes is thought to have 60 percent
of them insured against fire...
- Probability Distributions [11/04/1997]
Supposing a million people, without reference to each other's choices,
each choose a 'random' number between 1 and 1,000,000...
- Probability: Five and Seven Card Stud [6/7/1996]
We are trying to figure out how to calculate the probability of getting
two pair and three of a kind in five and seven card stud.
- Probability for Correctly Guessing a Random Color [11/16/1995]
There are six choices for a color I'm thinking of. Someone guessed my
color correctly, and then guessed again. She guessed correctly the second
time and did this again, and again, and again, and again. What is the
probability of this happening - that someone could guess correctly in a
- Probability in a Dice Game [01/04/2000]
How can I find the probability of each player winning, and the most
likely length of the game, for a dice game that may continue forever?
- Probability in Craps Game [6/27/1996]
Find the probability that the shooter will win in a game of craps.
- Probability in Flipping Coins [2/25/1996]
Six pennies are flipped. What is the probability of getting two heads and
four tails? Etc.
- Probability Interior Angles are Positive Integers [09/19/2001]
Find the probability that the measure of an interior angle of a regular
n-gon is a positive integer if n is an integer and 3
- Probability in the Infinite Plane [03/29/2003]
Three randomly drawn lines intersect so as to form a triangle on an
infinite plane. What is the probability that a randomly selected point
will fall inside that triangle?
- Probability in Virus Testing [06/04/1999]
What is the probability that an individual who has a positive test result
for the EB virus actually has the disease?
- Probability Involving Gender of Children [04/18/2005]
If a family plans to have six children, and the probability that a
particular child is a girl is 1/2, find the probability that the six
child family contains exactly two girls.
- Probability in Yahtzee [03/20/2002]
What is the probability of rolling two of a kind three times? four of a
kind? all five the same on the first roll? again on the second?
- Probability: Marbles, Coins, Cards [05/24/1997]
A series of questions about probability, permutations, and combinations.
- Probability of a Function Having Complex Roots [05/11/2000]
What is the probability that the function f(x) = x^2 + px + q = 0 will
have complex roots when p and q lie between 0 and 1? ...when p and q lie
between 0 and 5? ...when p and q are greater than 0?
- Probability of an Even Number of 6's [05/03/2003]
A fair die is thrown n times. Show that the probability that there is
an even number of sixes is 1/2 * [1+(2/3)^n].
- Probability of a Straight Flush [5/15/1996]
Finding the probability of drawing 5 spades, that is P(a flush) =
(13 12 11 10 9)/(52 51 50 49 48) P(flush of any
suit) = 4 P(a flush): the question is, what does the
P(Straight flush) = ?
- Probability of a Sum Meeting a Condition [08/24/2007]
Two real numbers from 0 to 12 are randomly chosen. Find the
probability that their sum is less than or equal to 5.
- Probability of at Least 45 Heads in 100 Tosses of Fair Coin [05/15/2004]
What is the probability of getting at least 45 heads out of 100
tosses of a fair coin? I have two different answers and I'm wondering
which, if either, is correct.
- Probability of a Triangle [12/10/1997]
If you cut a ruler with two arbitrary cuts, what is the probability of
creating a triangle?
- Probability of Being Struck by Lightning [8/23/1995]
While all 3.4 million secretaries were at the annual secretaries' day
picnic, a vicious storm began. Lightning headed directly for the
secretaries. Given that males are eight times as likely to be hit by
lightning as females, what is the probability that one of the male
secretaries will be struck?
- Probability of Choosing a Face Card [05/08/2001]
If you pick a card from a regular deck of cards (52), what is the
probability of getting a face card three times in a row?
- Probability of Continuous Random Variables [04/23/2003]
My book says that for any continuous random variable X, P (X=x)=0.
Using calculus, I can figure out the probability is 0, but by
intuition, I can't see why.
- Probability of Divisibility [06/18/2002]
What is the probability that a randomly selected three-digit number
is divisible by 5?
- Probability of Drawing an Ace [5/31/1996]
If I had 40 cards and there were 4 aces in the deck...
- Probability of Duplicate Pairs [05/13/2003]
Find the probability of getting at least 20 duplicate addresses when
drawing a sample of 30,000 at random from UK households (estimate
21,000,000) where there is replacement every time a selection is made.
- Probability of Forming a Triangle [01/24/2001]
A rope one unit long is cut in two places. What is the probability that
the three resulting pieces can be arranged to form a triangle?
- 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?