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Suppose we roll a dice (with 6 sides) 21 times.

What are the odds of getting either 1 or 2 an even amount of times?

I tried to calculate it by representing the number of times we get 1 or two as a binomial variable $B(n=21, p=\frac{1}{3})$, And summing the probability of getting $0, 2,\ldots, 20$ and I get the probability is $0.5$, which from what I saw in a different way of calculation is wrong.

Where did my method go wrong?

Brian Britos Simmari
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davidalk
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    Welcome to Mathematics SE. Take a tour. https://math.stackexchange.com/tour You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link https://math.meta.stackexchange.com/questions/9959/how-to-ask-a-good-question for further guidance. – SomeCallMeTim Feb 08 '23 at 16:37

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