Answer:
P(−2≤X≤1) = 5/9.
Step-by-step explanation:
Given:
P(-2≤X≤1) and he random variable X is the number on the red cube minus the number on the blue cube
x = -2. -1. 0 and 1
Let's take first number as in the red cube and the second number is in blue cube.
We get x = -2 for the following outcomes
(1, 3), (2, 4), (3, 5), and (4, 6). which is 4 favorable outcomes.
We get x = -1, for the following outcomes:
(1, 2), (2, 3), (3, 4), (4, 5), and (5, 6). which is 5 favorable outcomes
We get x = 0, when (1, 1) (2, 2)(3, 3)(4, 4) (5, 5),(6, 6) which is 6
We get x = 1, when (2, 1), (3, 2) (4, 3) (5, 4) (6, 5), which is 5.
The number of favorable outcomes= 4 + 5 + 6 + 5 = 20
The number of possible outcomes = 36 (when we toss the two dices, the possible number of outcomes is 36)
The required probability P(−2≤X≤1) = The total number of favorable outcomes / the total number of possible outcomes
= 20/36
P(−2≤X≤1) = 5/9.
Hope this will helpful.
Thank you.
