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

Answer 1

someone please help

Answer 2

I'm not sure what part (a) is about.
But if A represents P(event A) and similarly for B,
you have (1/2 * 1/2 + 1/2 * 1/2)^2 = (1/4 + 1/4)^2 = (1/2)^2 = 1/4

If that's not what A and B represent, you have, more generally,
(A/2 + B/2)^2 = A^2/4 + B^2/4 + 2 AB / 4 = A^2 / 4 + B^2 / 4 + AB / 2


For part (b):
Roll one of the cubes.
The top facing number will be
either from {1 5 6} or {2 3 4} - it doesn't matter which.
Then you want the other one to have its top face come from the other trio of numbers,
so P(success) = 3/6 = 1/2

You could work out the formula with a longer computation:
P(156 & 234) + P(234 & 156) =
2 * (1/2 * 1/2) = 2 * 1/4 = 1/2

Answer 3

thanks

Answer 4

np