MHB Probability Issues? Help Solving Joe's Die Problem

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Joe's problem involves calculating the probability of rolling a 1 at most once in four throws of a die, which fits the criteria for a binomial distribution. The key parameters include the probability of success (p) for rolling a 1, which is 1/6, and the number of trials (n), which is 4. To find the probability of getting a 1 at most once, the binomial probability formula can be applied. The discussion emphasizes understanding binomial distributions, including the importance of independent trials and fixed outcomes. This problem serves as a practical application of probability concepts in learning.
dann
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Having terrible time learning probabilities - so this question threw me.
Joe throws a die 4 times, what is probability of him getting a number 1 at most once? Hope you can help - learning binomial formulas, poisson & hypergeometric. Hope someone can assist.
 
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Well, this situation satisfies the four criteria for a binomial distribution:

Binary: the trial has to have a "success" (getting a 1) or "failure" (not getting a 1).
Independent: the trials have to be independent, one from another.
Number: the number of trials has to be fixed.
Success: the probability of success has to be the same from trial to trial.

So, what is the parameter $p$, and how many trials $n$ are there?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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