Question

Suppose you are playing a game with two number cubes. Let A represent rolling 2, 3, or 4, and B represent rolling 1, 5, or 6.
The probability of A is 1/2 and the probability of B is 1/2.

simplify (1/2A + 1/2B)
and
What is the probability that one number cube shows 2, 3, or 4, and the other shows 1, 5, or 6?

Answer 1

Not totally certain what the first question is asking. I suppose it could mean:
(1/2p(A) + 1/2(p(B)) = (1/2*1/2 + 1/2*1/2) = .25 + .25 = .5

As for the second question, I'm quite certain of this. The first die WILL be some number 1-6. Now, to get the situation desired, we just need the result of the second die to be one of the numbers in the other group. For example, if the first die is a 1, we want the second die to be a 2, 3, or 4. If, however, the first die is a 2, then we want the second die to be a 1, 5, or 6. Either way, there are 3 "good" options for the second die out of 6 total options.