Problem Solving

parveen110 wrote:
My approach:

6/6 * 1/6 * 5/6 * 4/6 = 5/54.

Where is this approach flawed?

You've essentially got:

First Die = Anything
Second Die = Same as first
Third Die = Different from first two
Fourth Die = Different from first three

This is a totally intuitive approach, but it's too restrictive: we don't have to be sure that the first two dice are the two that match. We also could have more than one pair, so we need to consider that scenario too.

Use complement.
P(at least one pair)=1-P(no pairs).
P(no pair)=4C2 (possible combinations of pairs) *P(one number)*P(of not that one number)*P(not the two previous numbers)*P(not three previous numbers).
P(no pair)=6*1/6*5/6*4/6*3/6=60/216=5/18
1-5/18=13/18