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Eduardo has a red 6-sided number cube and a blue 6-sided number cube. The faces of the cubes are numbered 1 through 6. Eduardo rolls both cubes at the same time. The random variable X is the number on the red cube minus the number on the blue cube. What is P(−2≤X≤1)? Enter your answer, in simplest fraction form, in the box

help asap

Mar 23, 2019

#1
+1

Let's take it case by case, for when X = -2, -1, 0, and 1. Also, let the form (a, b) mean the number a on the red and b on the blue.

When X = -2, we can have (1, 3), (2, 4), (3, 5), and (4, 6).

When X = -1, we can have (1, 2), (2, 3), (3, 4), (4, 5), and (5, 6).

When X = 0, this is just doubles, so it is just when a = b, or 6 ways.

When X = 1, we just reverse a and b when X was -1, to get another 5 ways. So, there are 4 + 5 + 6 + 5 = 20 ways. To find the probability, there are 6 x 6 = 36 ways total, so the answer is 20/36 = 5/9.

Hoping this helped,

asdf334

Mar 23, 2019
#2
+1

Thank you very much for explaining it step by step! LMessiA  Mar 23, 2019