I am requesting assistance on the followingproblem. What is the probability that

Question

I am requesting assistance on the followingproblem.
What is the probability that you win a lottery with a three-digitnumber, given that you have two digits of the winningnumber?
The way I figured this should work would be that initially,your chance of winning is 1:1000 - (1/10 x 1/10 x 1/10).
If I have 2 numbers of the winning number, then theprobability that I win the 3-digit lottery is 1/10. I am requesting assistance on the followingproblem.
What is the probability that you win a lottery with a three-digitnumber, given that you have two digits of the winningnumber? The way I figured this should work would be that initially,your chance of winning is 1:1000 - (1/10 x 1/10 x 1/10). If I have 2 numbers of the winning number, then theprobability that I win the 3-digit lottery is 1/10.

Explanation / Answer

I'm assuming you have two digits but you don't know which digit inthe number it occurs. So assume the two digits you know are x andy, the possible winning numbers are - xyk, yxk, xky, ykx, kxy, kyx where k is any of the 10 random digits. Thus there are sixtypossibilities (10 for each of the 6 combinations above) with equallikelihood, so your chances of getting them right are 1/60.

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