Question

Four candidates are running for mayor of Happyville. According to the polls candidate A has a​ "one in ​" probability of winning​ [that is, ​Pr(A)​1/​]. Of the other three​ candidates, all we know is that candidate C is as likely to win as candidate B and that candidate D is as likely to win as candidate B. Find the probability assignment for this probability space.

Answer 1

The probability assignment for this probability space is Pr(A) = 1/, Pr(B) = /3, Pr(C) = /3, and Pr(D) = /3.

Step-by-step explanation:

To find the probability assignment for this probability space, we need to determine the probabilities for each candidate. Let's assign the probabilities as follows:

• Pr(A) = 1/
• Pr(B) = x
• Pr(C) = x
• Pr(D) = x

We know that candidate A has a probability of 1/ of winning. The question states that candidate C is as likely to win as candidate B and candidate D is as likely to win as candidate B. This means that Pr(B) = Pr(C) and Pr(B) = Pr(D). Since the probabilities must add up to 1, we can set up the equation:

1/ + x + x + x = 1

Combining like terms, we have:

1/ + 3x = 1

Subtracting 1/ from both sides:

3x = 1 - 1/

Simplifying, we get:

3x = /

Dividing both sides by 3:

x = /3

Therefore, the probability assignment for this probability space is:

• Pr(A) = 1/
• Pr(B) = /3
• Pr(C) = /3
• Pr(D) = /3