You're playing a game in which the probability of winning each round is.20.
on average, how many rounds do you have to play to first win?

The chance of losing five games in a row is 0.8 × 0.8 × 0.8 × 0.8 × 0.8 = 0.85 = 0.328. The chances of that not happening is 0.672. That’s the chance that you will win at least one game out of the five. 67.2%.

Much later:

I just noticed that this question had details that are now in a comment:

I already know the technique: 1 - (0.8)^5

But I wanted to know how to do it in other ways

Sadly Quora no longer shows the question details below the question the way it used to. My answer explained it in the way the asker indicated in their comment that they already knew and they wanted something different. Sorry about that. At this point, I’m not inclined to try figuring out other ways (enumerating all the sequences, for example, and tallying the probabilities).

Step-by-step explanation:

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step-by-step explanation:

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step-by-step explanation: