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Browse College Probability

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See also College Statistics.

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 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 Multiple Failures [06/20/2002]
If two components have average lifespans of 2500 hours, and the probability of failure for each is f(t) = (1/u)e^(-t/u), what is the probability (1) that both components will fail within 2500 hours, and (2) that both will fail within a total of 2500 hours of operating time?

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?

Probability of Repeating Digits [11/8/1994]
A native speaker of German writes: The decimal representation of a real [number] can be viewed as pseudo-random because it's not ending and not repeating. If you take any real, what is the probability of finding 987987987 in the decimals?

Probability of Typing a Sonnet [9/2/1996]
Statistics, God, and the probability of life arising by "pure chance"...

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 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 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 Using Geometric Random Variables [01/15/2004]
Let X be a geometric random variable with parameter p1 and let Y be a geometric random variable with parameter p2. Find the probability that X is less than or equal to Y.

Probability with a Weighted Coin [04/12/2001]
Find the probability of getting three heads in a row with a weighted coin, with a 1/3 probability of getting a head on each toss. What if I want to be 99% sure of getting three heads?

P-Value Calculation [04/12/1997]
I am able to determine the chi-square value, but I do not know how to determine the p-value, or if I can even do that.

Question on Probability of Repeating Digits [04/18/2001]
You said that the probability is 1 that you can find any number with that string in it. I don't understand how.

Random Card Shuffling Probabilities [6/11/1996]
What is the probability of at least two eights being next to each other in a random shuffling of a deck of cards. What about at least two cards (2 eights or 2 queens etc.) being next to each other?

Randomly Cutting a Rope into Two Segments [05/14/1998]
A rope 20m long is randomly cut into two segments, each of which is used to form the perimeter of a square . . .

Random Variables and Order Statistics [08/16/2001]
Let X1, X2, ....., Xn be n independent and continuous random variables with the same distribution, let X denote the maximum and Y the minimum of these random variables, and let U = X / Y; find the distribution of X,Y, and U.

Random Walk Coin Simulation [10/27/2005]
A game starts with a score of zero, and adds or subtracts one based on whether coin flips come up heads or tails. Is there a way to calculate how many coin tosses it will take to reach a score of n or -n?

Random Walk Problem [04/10/2006]
What is the probability that Dorothy doesn't fall off the cliff if she starts one step away from it and moves backwards and forwards one step at a time depending on the toss of a coin?

Regression Analysis of Four-Parameter Data [01/21/2000]
How do I perform a regression analysis on four-parameter experimental data to determine the values of A, B, C and D in the equation y = [(A- D)/(1+{x/C}^B)]+D?

Riemann, Mayan Math [5/20/1996]
Math projects: A. Riemann - a German mathmatician; B. The Mayan number system and calendar; C. Probability.

Rolling Dice and Probability [11/07/2007]
If I roll a die 10 times, what is the probability that I will have gotten all numbers from 1 to 6 at least one time each?

Runners and Heart Attacks [01/14/1997]
Given data regarding the occurrence of heart attack among runners and non-runners, determine whether there is a connection between runner status and heart attacks.

Running Shoes [02/07/2001]
What proportion of the time does the runner run barefoot?

Sharing a Zodiac Sign [04/24/2001]
In a class of 35 students, what is the probability that every student in the class will have the same zodiac sign as at least one other classmate?

Social Security Number Probability [02/09/2004]
What are the chances that a 9-digit Social Security number is comprised entirely of 2 digits, such as 211-12-1221?

Stochastic Matrices [03/17/1998]
Finding the transtion matrix and steady-state vector of a stochastic process.

Stocks and the Binomial Distribution [12/09/1998]
If an index of stock prices has probability 0.65 of increasing in any year, how can you turn this into a binomial distribution question?

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?

Ten Coin Flips, Four Heads [05/08/2001]
If you flip a coin ten times, what is the probability of getting at least four heads?

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 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?

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 circle?

The Two Envelope Paradox in Probability and Expected Return [09/20/2005]
A classic problem in which two envelopes contain money, one double the other. After choosing one at random, should you trade it for the other? It appears there should be no advantage, but the expected values suggest otherwise. Or do they?

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 Random Variables, Each Correlated to a Third [04/29/2003]
If X, Y, and Z are 3 random variables such that X and Y are 90% correlated, and Y and Z are 80% correlated, what is the minimum correlation that X and Z can have?

Uniform and Exponential Distribution of Random Variables [01/16/2006]
Can you prove that if you take the natural log of a uniformly distributed random variable, it becomes a exponentially distributed random variable?

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?

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