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Dr. Math FAQ:
probability in the
Browse High School Probability
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Selected answers to common questions:
Odds vs. probability.
- 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 Dice Tosses, All Pairs? [10/16/2017]
An adult wonders about the likelihood that ten dice tosses yield a matching pair each time. With tree diagramming, Doctor Ian reveals patterns and a path forward.
- 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
- Test for Tuberculosis [07/28/1997]
A test for tuberculosis was given to 1000 subjects, 8 percent of whom were
known to have tuberculosis... what is the probability of a randomly
selected person having tuberculosis...?
- Theoretical and Experimental Probability [05/07/2001]
If we spin a spinner 20 times and record the results, what might we
conclude from our experiment?
- Theory of 'Runs' [8/20/1996]
If all possible orders of 20 people are considered, what is the average
value of the number of places in the row...?
- Three Fair Dice [05/16/1999]
Find the probabilities of a total of 9 and a total of 10 when three fair
dice are tossed once... Compare...
- Three Heads in a Row [01/25/2001]
How many flips of a coin on the average will it take to get three heads
(or tails) in a row?
- Three People Toss a Coin [03/22/2002]
Three people each toss a coin in order. The winner is the first to get a
'tail'. Expressed as fractions, what are their respective chances of
- Three Pieces of a Stick Forming a Triangle [01/22/2007]
If you break a straight stick into three pieces, what is the
probability that you can join the pieces end-to-end to form a triangle?
- Three Share a Birthday [09/17/1999]
What is the probability that in a class of 24 students, 3 of them will
share the same birthday?
- Throwing Dice More Than Once [09/25/1997]
If I throw one die once the probability of getting any one of the six
numbers is 1/6. Does this change if I throw more than once?
- Tie Combinations [05/31/1999]
If four people have three identical ties, what is the total number of
different combinations the four can wear, and what is the probability
that all four people will wear the same tie?
- Tips on Solving Probability Problems [08/27/1999]
Questions about probability distribution involving means, standard
deviations, Poisson distributions, independent random variables and
- Toss a Coin Six Times [02/07/1998]
Suppose a coin is tossed 6 times - what is the probability that 3 heads
- Tossing a Coin and Rolling a Die [11/14/2002]
If you toss a coin and roll a die, what is the probability of
obtaining: a) heads and a five b) heads or a five c) tails or a two?
- A Triangle in a Circle [05/26/2000]
Suppose you randomly place 2 points on the circumference of a circle.
What is the probability that a 3rd point placed randomly on the circle's
circumference will form a triangle that will contain the center of the
- Triangle Inequality [09/14/1997]
Suppose that you have a straight pipe cleaner of a given length. The two
ends are points A and C...
- A Truck and a Van [07/11/1999]
A small cartage company has two vehicles, a truck and a van... what
proportion of the time is the van used?
- True/False and Multiple Choice Tests [05/24/1999]
What is the probability of passing a 20-question true/false test by
- Twist on Monty Hall [03/31/2001]
You can open as many of the doors as you like, but you have to stay with
the last door that you open...
- The Two Envelopes [09/08/1997]
Given two sealed envelopes, one containing twice as much money as the
- Two-Headed Coin and Bayesian Probability [04/21/2003]
In a box there are nine fair coins and one two-headed coin. One coin
is chosen at random and tossed twice. Given that heads show both
times, what is the probability that the coin is the two-headed one?
What if it comes up heads for three tosses in a row?
- Two Heads After N Tails [05/20/1999]
What is the probability of flipping two heads after n number of tails?
- Two Probability Questions [06/08/1999]
What is the probability that all customers will get the type of butter
they want? ...that every person who shows up for the flight will get a
- Tying Up Loose Ends to Create Different Size Loops [10/3/1995]
Wandelina has six identical pieces of string held firmly in her fist,
with one end of each sticking out above her fist, and the other end of
each sticking out below her fist. Different people come along and tie the
ends above her hand together, and tie the ends below her hand together.
When Wandelina opens her fist and looks at the strings, what combinations
of different size loops might there be? What is the probability of each
possible combination occurring?
- Understanding Probability [05/13/2002]
If I were looking for a probability of colored marbles in three
packages, how would I do that?
- Using a 6-sided Die to Generate a Random Number From 1 to 7 [12/23/2007]
I need to choose one of seven cards at random in a card game. Is there
a way I can use a 6-sided die to be sure that my pick is truly random?
- What If You Paint the Balls? [03/25/2002]
Given 800 blue balls in a bag, you take out 35 of them, paint them red,
and replace them. Do this 23 times and you *might* paint all of them -
what are the odds?
- What is a Biased Die? [03/01/2002]
How do we find the probability when the dice are biased?
- What Is N Factorial Used For? [08/29/2001]
I have heard that it is used in probability, but what for, and how?
- What is the Meaning of "Average"? [03/28/2007]
An interesting conversation that defines the general concepts of
average and central tendency, and looks at the usefulness of such
measures both in representing the data and for making predictions
about future events.
- What Makes Events Independent? [06/03/2002]
Why, after tossing 10 heads in a row, isn't the next toss more likely
to come up tails?
- What's the Probability That Two Will Agree? [11/10/1997]
Of the nine members of the board of trustees of a college, five agree
with the president. The president selects three trustees at random and
asks their opinions...