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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.
- Coin Flipping [01/26/1998]
How can I figure out the chances of flipping a coin five times with the
- Coin Landing on Edge [11/20/2001]
Is there a way to calculate the odds of a coin dropped from a known
height landing on its edge rather than heads or tails?
- Coin Landing on Edge [11/29/2001]
What are the chances of a coin landing on edge? A Canadian copper penny,
- Coin Tosses, Dealing Cards... [12/08/1998]
Several questions on discrete math - probability and combination;
deducing recurrence relations.
- Coin-Tossing Game [05/09/2001]
Three men toss a coin in succession for a prize to be given to the person
who first obtains a head. What is each man's chance of winning the prize?
- Collecting a Complete Set [03/15/2000]
I have a very large box filled with 8 different frying pan handles in
equal proportions. What is the probability that I will have to remove 32
handles before I get a complete set?
- Collecting a Set of Coupons [02/03/2000]
Given N different types of coupons, what is the expected number of
different types of coupons that are contained in a set of (n) coupons?
What is the variance and the expected number of coupons one one needs to
collect before obtaining a complete set?
- Colored and Numbered Discs [05/25/2001]
Drawing colored and numbered discs from boxes; rolling colored and
- Combinations of Married Couples [11/08/1996]
What is the probability that 12 people can be grouped into 6 pairs where
each pair is a married couple?
- Combinatorial Probability Tournament [01/23/2002]
A tennis tournament for 2^n players is organised as a knock-out
tournament with n rounds, the last round being the final. Two players are
chosen at random. Calculate the probabilities they meet a) in the first
round; b) in the final; c) in any round.
- Complex Ratio Problem [07/31/1997]
If you randomly throw 3 points on a plane, you get a triangle... What is
the probability that the triangle will become obtuse...?
- Conditional Probability [05/25/2000]
Suppose used car salesmen tell the truth 2/5 of the time, and 1/3 of the
trees in a forest are oak...
- Conditional Probability [12/31/1997]
I tutor probability and statistics and people seem to be confused by the
use of the multiplication rule in conditional probability...
- Consecutive Failures in Bernoulli Trials [07/07/1999]
What is the probability that out of n experiments there will be a string
of at least k experiments in a row that fail?
- Contest Probabilities [10/14/1998]
Players of equal skill meet in an elimination contest. With n players,
what is the probability that a player will compete in i rounds?
- Craps [5/24/1996]
Can you give me information on the probability and outcome of the game
- Creating a Mathematical Model of a Complicated Situation [10/09/2005]
I am riding a bike and have several possible routes, each of which
contains various traffic lights, amounts of traffic, the possibility
of being stopped by a policeman for running a light, and other factors
which influence the time it will take to ride each route. How can I
model the routes to predict which will be the best choice?
- Cupcakes and Boxes: Conditional Probability [01/03/2002]
Given 3 boxes, each with 2 cupcakes (1 box has two vanilla, 1 has 2
chocolate, and 1 has one of each). A box is selected randomly and a
cupcake is selected that turns out to be chocolate. What's the
probability that the other cupcake in that box will be chocolate?
- Darts and Wilensky's Paradox [03/17/1999]
What is the probability of scoring 25 points with 2 darts if the
dartboard is made up of 4 concentric circles?
- Defining Independent Events [07/14/2009]
My book says two events E and F are independent if P(E|F) = P(E). Do
we also have to have P(F|E) = P(F) or does this automatically follow?
Could there be a situation where P(E|F) = P(E) but P(F|E) =/= P(F)?
- Defining Probability [4/30/1996]
Is a probability number equal to a percent or a decimal?
- Definite Integral of e^(-x^2) and e^((-x^2)/2)) [08/18/1999]
How can I find the integrals of e^(-x^2) or e^((-x^2)/2)) from x = 0 to
- Deriving the Normal From the Binomial [07/11/1998]
How is the normal distribution derived from the binomial distribution?
Does the normal approximate the binomial?
- Dice: Full House [6/28/1996]
What is the probability of rolling a full house with 5 six-sided dice?
- Dice Game and Expected Value [04/18/2005]
You pay $6 to play a game where you roll a die with a payoff as
follows: $8 for a 6, $7 for a 5, and $4 for any other result. What are
your expected winnings? Is the game fair?
- Die Roll Probabilities in Gaming [01/06/2001]
Players fight battles by rolling two dice and adding modifiers according
to each player's advantages. Generate a chart giving the odds of victory
based on modifiers.
- Distribution of Cards in Bridge [05/03/2001]
In bridge, it often happens that you and your partner have 9 cards of a
suit between you. In all the bridge books that I have read, it is stated
that the probability of the remaining 4 cards splitting 2-2 is 40.7%. Can
this be proven?
- Do Prior Outcomes Affect Probabilities of Future Ones? [05/26/2008]
I know that the probability of flipping a coin and getting a head is
1/2. But if I've gotten ten straight tails, isn't it more likely that
the next one will be a head?
- Drawing Aces [06/12/1997]
What is the probability that you will pick two aces in a row out of a 52-
- Drawing Marbles [05/05/1998]
A jar contains 19 different marbles. I draw 13 marbles, one at a time,
but replace the marble back before taking the next....
- Drawing Prizes [07/06/2003]
If there are many cheap prizes, does the probability of getting a good
prize go up as more prizes are drawn?
- Drunk Drivers and Traffic Deaths [05/14/1997]
Knowing the total traffic fatalities and the number involving alcohol,
what is the probability that a traffic death may be attributed to
- Empirical and Mathematical Probabilities [12/04/1998]
What is the difference between empirical probability and mathematical
- Empirical Probability [01/15/1999]
If I flipped a coin 10 times and got heads each time, would the
probability of a head on the next flip be 1/2 or almost 1?
- English Exam Probability [12/17/2001]
Given a list of 25 potential exam questions, with 10 of them on the
actual exam and of which students write essays on 2, how many questions
should be prepared to be 95% confident you won't write on a question you
- Even Number of Heads [02/12/2002]
What is the probability of getting an even number of heads when tossing a
- Executive Committee Vote [01/21/1997]
124 delegates must elect a 13-member executive committee from a list of
26 candidates. If each delegate votes for 10 candidates, what is the
least number of votes a candidate can get and be elected?
- Expected Tosses for Consecutive Heads with a Fair Coin [06/29/2004]
What is the expected number of times a person must toss a fair coin to
get 2 consecutive heads?
- Expected Value [12/09/1997]
What is expected value?
- Expected Value [11/07/2001]
I am playing a game where I toss a fair coin. I get a bead if I flip a
head and I lose a bead if I flip a tail... to get a total of 5 beads,
what is the expected number of coin tosses I must make?