Question

I have to find the probability that when three dice are rolled at the same time, the largrest value of the three numbers rolled is 4. Let A be the outcome in which the largest number is 4, let B be the outcome in which the largest number is 4 or less, and let C be the outcome in which the largest number is 3 or less. Let P(X) denote the probability tha the outcome of an event is X. Then , I have to calculate P(B), P(C) and Since B=A U C and the outcomes A and C are mutually exclusive, calculate P(A)

Answer 1

So, a lot of probability relies on interpreting the question. In this case, I interpret the question as follows(although the first part is different, which does cause some problem as to what you are asking):
P(A) >4
P(B) =<4
P(C) =<3
P(A) > 4 = 2/6 (i.e. that you get the numbers 5 and 6)
P(B) = <4 = 4/6 (i.e that you get either 4, 3, 2 or 1)
P(C) =<3 = 3/6 (i.e. that you get either 3, 2 or 1)
combining these we get:
P(A) and P(B) and P(B) = 2/6 x 4/6 x 3/6 = 24/216 (or 12/108 or 3/27)
however, I would like some other more experienced folks to weigh in on this problem before you accept the solution.

Answer 2

@dan816