Hello,

I was having a problem understanding a Quant probability question on GregMat and would extremely appreciate if someone can explain certain parts of it. The problem and Greg’s solution can be seen below:

A die is thrown at most 7 times until we get an odd number.

What is the probability of **only** the last throw being odd when the die is thrown an even number of times?

Can someone explain why is Greg adding up all the probabilities at the end? Shouldn’t it instead be the sum of numerators ( 1 + 1 + 1 = 3 ) divided by the sum of denominators ( 4 + 16 + 64 = 84), which would equal to 3/84 = 1/28 probability. Instead the answer implies that there are 21 ways to get an odd number last, while we clearly see there are only 3 ways.

Please tell me where I am wrong, since it seems that I am completely inept with probabilities.

Thanks