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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.

Closed Envelopes Paradox [09/13/2001]
You must choose between two closed envelopes, one with a certain amount of money and the other with twice as much...

Coin Flipping [01/26/1998]
How can I figure out the chances of flipping a coin five times with the result T,T,T,H,H?

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, round.

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 numbered dice.

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 by Degrees [01/08/2016]
A teen faces a word problem, and seeks clarity on its combinations ... or are they permutations? By diagramming a simpler probability scenario and then building it up, Doctor Ian models where the powers come from.

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 craps?

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 1.96?

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- card deck?

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 drinking...?

Empirical and Mathematical Probabilities [12/04/1998]
What is the difference between empirical probability and mathematical probability?

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 haven't prepared?

Even Number of Heads [02/12/2002]
What is the probability of getting an even number of heads when tossing a biased coin?

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?

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