Hi All,

'A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number'?

The author goes on to explain the strategy to answer....

1. Set the result of the first die to be any number. * This will allow us to concentrate on matching the second and third die to the first, is that correct?

2. Prob of Second matching first, Third not matching = [tex]\frac{1}{6}.\frac{5}{6}[\MATH]

* There is a one in six chance of the second matching as there are 6 digits, is that correct? There is a five in six change of the Third not matching as [tex] 1 - \frac{1}{6} = \frac{5}{6}. [\MATH]Is that correct?

This is where it gets really confusing.

3. Prob of Third matching first, second not matching = [tex]\frac{5}{6}.\frac{1}{6} [\MATH]

* I can't figure out where this fractions came from. As above, matching = [tex]\frac{1}{6}[\MATH]

4. Prob of second and third matching each other = [tex]\frac{5}{6}.\frac{1}{6}[\MATH]

* as with 3. I can't figure out where these probabilities came from.

I understand the logic to this approach it's just the specifics I'm struggling with.

N.B. Latex does not seem to be compiling for me so forgive the [\MATH]. I hope it makes sense.

Thanks in Advance,

D