Question

Bob, the proprietor of Midland Lumber, believes 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? (Round your answer to three decimal places.)

Answer 1

There is a 35.7% probability that this deal will not materialize.

Explanation:

This problem can be solved by a simple system of equations.

-I am going to say that x is the probability that this deal materializes and y is the probability that this deal does not materialize.

The sum of all probabilities is always 100%. So

`1) x + y = 100`.

Bob, the proprietor of Midland Lumber, believes that the odds in favor of a business deal going through are 9 to 5.

Mathematically, this means that:

`2) (x)/(y) = (9)/(5)`

We want to find the value of y. So, we can write x as a function of y in equation 2), and replace it in equation 1).

Solution:

`(x)/(y) = (9)/(5)`

`x = (9y)/(5)`

`x + y = 100`

`(9y)/(5) + y = 100`

`(14y)/(5) = 100`

`14y = 500`

`y = (500)/(14)`

`y = 35.7`

There is a 35.7% probability that this deal will not materialize.