Two player play a game with two nonstandard dice A and B A h

Two player play a game with two nonstandard dice A and B. A has 4 sides which show 5 and the rest show 2 while B has 3 sides which show 7 and the rest show 0. When rolled, each face is equally likely to show. If player 1 rolls A and player 2 rolls B, what is the probability that player 1 rolls a higher number than player 2?

Solution

Prob of Player A rolling 3 = 1/2 and then Player B rolling 2 = 1/2 So, net prob = 1/2*1/2 = 1/4

Prob of Player A rolling 6 = 1/2 and then Player B rolling 2 = 1/2 So, net prob = 1/2*1/2 = 1/4

So, answer = 1/4 + 1/4 = 1/2