[Math] The Number of Times a Coin Needs to Be Flipped Until Head Appears

expectationprobability

I need to find out the number of times a fair coin is needed to flipped, until head appears for the first time.

Now, the options are: 2, 8, 16, and 64.

I don't think it can be calculated. Because every time a coin is flipped, the chance of head appearing is .5 or 50%.

How to calculate this?

Edit: I wrote the question according to the original question I found. The title was written accordingly. Seeing an experienced user's edit on my question, I guess the correct title is: 'The Average Number of Times a Coin Needs to Be Flipped Until Head Appears'.

Best Answer

geometric distribution $E=\cfrac{1}{p}$. Or by definition of expectation:

$0.5\times 1+0.25\times 2+0.125\times 3+\cdots+0.5^k\times k+\cdots=2$

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