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If i flip a coin 10 times, what is the probability of getting heads on the 10th flip ? or on the second flip ? what is the math formula ?

Each coin flip is independent. Flipping one coin 10 times is the same as flipping 10 different coins at the same time and looking at all of the results. We know that a single coin will land on heads 50% of the time and tails on the other 50%. That's for 1 coin flip. Now, as we said before, each coin flip is independent of each other. That means, the second, third, fourth, etc. coin has the same chance as the first to be either heads or tails.

The 1st coin flip is 50%, the second is 50% and the tenth is also 50%. It's all the same as one single coin flip.

it shore looks like that but something is not logical

bet 1 | $2
bet 2 | $4
bet 3 | $8
bet 4 | $16
bet 5 | $32
bet 6 | $64
bet 7 | $128
bet 8 | $256
bet 9 | $512
bet 10 | $1024

On a 10 bets game like this you can win $1024 or you could lose your $1

So it does not make sense that each event is independent ... and last bet probability of getting heads is 50%

My instinct / gut is telling me that 50% chance for last bet is false ...

I think your question is different from what you're asking then. Are you asking: what is the probability I can win $1024 on the 10th round?

This is different from the coin question. If you're asking the chance of winning a coin flip back to back 10 times, then you calculate as such:

On each round you have a 1/2 chance of winning or doubling your initial bet. This is because it's a coin flip.

However, now you need to keep in mind that you need to win all of these in a row. As in, you need a coin flip to be heads on the first, second, third, etc. flips. This means out of 10 flips, all 10 must be heads to double your money.

In the case that we have 10 flips and each flip has a 1/2 chance of giving you a payout, we have (1/2) * (1/2) * (1/2) ... ten times, or (1/2) ^ 10 which is a 0.0009765625 chance of doubling your money 10 times in a row.

nice, finally a good answer ... sry if question was wrong ...i am not a english native speaker

so it's 1/1024 chance ... thank you for answer

No problem! Grin