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Browse College Probability

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See also College Statistics.

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?

Variance Existence: Biased by Normalcy? [10/06/2016]
An adult struggles to understand why some variances do not exist. Suspecting that our experiences with the normal distribution may have biased our expectations, Doctor George points out that some probability density functions even have an undefined mean — including the Cauchy distribution.

Visually Identifying Mean of a Probability Density Function [03/06/2007]
When looking at the graph of a probability density function, I know the mode is the highest value it reaches, and the median splits the area under the curve equally, but how can you find the mean visually?

Waiting Time Distributions [06/08/1997]
What are waiting time distribution tables and how do you solve them?

Weather Forecasting [05/24/1997]
If the weather is dry one day, show that the probability that it will be dry n days later satisfies Pn = (2p - 1)Pn-1 + (1 - p) and P0 = 1.

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'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...

Yahtzee Probabilities and a State Matrix [12/30/1998]
In Yahtzee, what are the odds of rolling 5 of a kind within 3 rolls of the dice? What if you reroll all 5 dice each time? Does this involve transition matrices?

Yahtzee Probability [07/20/2009]
What are the odds of rolling a Yahtzee on three consecutive turns where each turn allows up to three rolls?

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