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Chapter 8: Problem 37

Bob, the proprietor of Midland Lumber, feels that the odds in favor of a business deal going through are 9 to 5\. What is the (subjective) probability that this deal will not materialize?

Short Answer

Expert verified
The subjective probability that the deal will not materialize is \(\frac{5}{14}\).

Step by step solution

01

Understanding the problem

Bob believes that the odds in favor of a business deal going through are 9 to 5. Odds are a ratio between the number of ways something can happen (success) and the number of ways it can't happen (failure). So in this case, 9 represents the number of ways the deal can go through, and 5 represents the number of ways it can't.
02

Find the probability of the deal materializing

To find the probability of the deal materializing, we can use the odds to calculate the ratio of successful outcomes to the total number of possible outcomes. The probability of the deal going through is given by: \(P(\text{deal materializing}) = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}}\) The total number of possible outcomes is the sum of the successful outcomes (9) and unsuccessful outcomes (5). So we have: \(P(\text{deal materializing}) = \frac{9}{9+5}\)
03

Calculate the probability of the deal materializing

Now, calculate the probability of the deal materializing: \(P(\text{deal materializing}) = \frac{9}{9+5} = \frac{9}{14}\)
04

Calculate the probability of the deal not materializing

To find the probability of the deal not materializing, subtract the probability of the deal materializing from 1: \(P(\text{deal not materializing}) = 1 - P(\text{deal materializing})\)
05

Calculate the probability of the deal not materializing

Plug in the probability of the deal materializing that we calculated in Step 3: \(P(\text{deal not materializing}) = 1 - \frac{9}{14}\)
06

Simplify the probability of the deal not materializing

Simplify the fraction to get the final probability: \(P(\text{deal not materializing}) = \frac{14-9}{14} = \frac{5}{14}\) So, the subjective probability that this deal will not materialize is \(\frac{5}{14}\).

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