# sudo wrote

I agree with you, but statistically, don’t your chances start over each time.

Yes, that is correct. For each *individual* coin flip, your odds are always 50% heads, and 50% tails. But, what we're talking about here are *multiple* coin flips. We want to know what the odds are of flipping a coin *twice*, and never getting heads. Here are all the possible outcomes, with H representing heads and T representing tails: (H, H), (H, T), (T, H), (T, T). You can see that there is only *one* outcome out of four that doesn't have any heads in it. So, the probability of flipping the coin twice and not getting heads 1/4, or 25%. Notice that if you multiply the individual chance (1/2) by itself however many times you're flipping the coin, you get the chance of never getting heads for that many coin flips. So, to flip it three times and never get heads has a chance of 1/2 * 1/2 * 1/2 = 1/8, or 12.5%. Four times is (1/2)^4 = 1/16, or 6.25%.

Let's say your odds of not getting caught while shoplifting are 99%. So, if you only plan to shoplift *once* in your lifetime, then you would go with the individual odds, or (99/100)^1. But, if you plan to shoplift 100 times, then you would go with (99/100)^100, which is a 36.6% chance of never being caught.

Did that make sense?

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