A die is weighted in such a way that each of 1 and 2 is eight times as likely to come up as each of the other numbers. Find the probability distribution. What is the probability of rolling an odd number? Step 1 We are given that a die is weighted in such a way that each of 1 and 2 is eight times as likely to come up as 3, 4, 5, or 6. We are asked to find the probability distribution associated with this die. The probability of each outcome is unknown, so the first step is to use the properties of probability distributions to write an equation that we can solve for the probability of one or more of the outcomes. Assign the variable x to the probability of rolling a 3, and compute the probabilities of the other outcomes, in terms of x.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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A die is weighted in such a way that each of 1 and 2 is eight times as likely to come up as each of the other numbers. Find the probability distribution. What is the probability of rolling an odd number?
Step 1
We are given that a die is weighted in such a way that each of 1 and 2 is eight times as likely to come up as 3, 4, 5, or 6. We are asked to find the probability distribution associated with this die.
The probability of each outcome is unknown, so the first step is to use the properties of probability distributions to write an equation that we can solve for the probability of one or more of the outcomes. Assign the variable x to the probability of rolling a 3, and compute the probabilities of the other outcomes, in terms of x.
 
p(3)=x
 
p(4)=p(5)=p(6)=__________
 
p(1)=p(2)=_________
 
Substitute the probabilities, in terms of x, in to the probability distribution.
Outcome 1 2 3 4 5 6
Probability 8x
 
 
 
x
 
 
 
x
 
 
 
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