User talk:Re-Intuition

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-- Recent uploads SpineTalkContribs 00:27, 16 July 2019 (UTC)

Motherlode Mine[edit source]

Your expected value is wrong because the summation you gave assigns a 4/27 chance to getting exactly 2, when in reality the chance is 2/3 * 1/3, or just 2/9. I think you realized that the summation gave the wrong probability for the k=1 case which is why you pulled out the 1/3 to the side. Your summation has an extra multiplicative 2/3 term in it, and the real formula you want is 1/3 + (sum (2/3)^(k-1)*k from k=2 to 26)/3, which gives the correct answer of 3. A simpler formula is (sum (2/3)^(k-1)*k from k=1 to 26)/3, or you can also intuit that you're "spending" one-third of the vein each time you get a pay-dirt, so each vein should be worth three. ʞooɔ 06:18, 17 July 2019 (UTC)