What are the odds of losing a bet 10 times in a row when I have a 25% chance of winning?

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I have been looking for an online calculator to solve the below 2 mathematical problems, but I haven't yet found such a calculator. Thus, can someone answer these questions for me?

1. What are the odds of losing a bet 10 times in a row when I have a 25% chance of winning?
2. What are the odds of losing a bet 20 times in a row when I have a 25% chance of winning?

edit: I mistakenly forgot to mention that I would like the reply answer to be in the equation of "1 in 1000" or "1 in 12,448" (or whatever the real answer is). I apologize for forgetting this important part.

I will appreciate any help I can get with the above 2 math questions.

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1 Answer

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First part:

Probability of losing 10 times in a row = $(1-0.25)^{10} = (0.75)^{10}$

$$\text{odds} = \frac{\text{favorable outcome}}{\text{unfavorable outcome}}$$

Here the probability of losing $10$ times in a row is favorable outcome, so

$\text{odds} = \frac{0.75^{10}}{1-0.75^{10}}$

Similarly, for second part:

$\text{odds} = \frac{0.75^{20}}{1-0.75^{20}}$

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