Question 1136593: A die is weighted so that the even number outcomes are twice as likely as an odd outcome. When the die is tossed each odd outcome is equally likely and each even outcome is equally likely. Find the probability that a 1 or 2 is tossed. Create a sample space and probability measure for this process.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Reasoning logically without any formal mathematics, a 1 is one of three possible odd number outcomes with equal probability, and 2 is one of three possible even number outcomes with equal probability. Therefore the probability of tossing a 1 or 2 with this weighted die is 1/3.
Mathematically, we have 6 outcomes, with three of the outcomes having twice the probability of the other three. So
(x+x+x)+(2x+2x+2x) = 1 --> x = 1/9
P(1) = x = 1/9
P(2) = 2x = 2/9
P(3) = x = 1/9
P(4) = 2x = 2/9
P(5) = x = 1/9
P(6) = 2x = 2/9
P(1 OR 2) = 1/9 + 2/9 = 3/9 = 1/3
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