Question

Suppose that the manager of a company has estimated the probability of a super-event sometime during the next five years that will disrupt all suppliers as 0.23%. In addition, the firm currently uses three suppliers for its main component, and the manager estimates the probability of a unique-event that would disrupt one of them sometime during the next five years to be 1.4%. What is the probability that all three suppliers will be disrupted at the same time at some point during the next five years

Answer 1

The probability that all three suppliers will disrupt = 0.0023

Explanation:

Below is the formula used to calculate the probability of disruption.

`P(n ) = S + (1 – S) U^(n) \\`

`S = Super \ event \\`

`U = Unique \ event \\`

`L = Loss \\`

`S = 0.23 \ Percent = 0.0023 \\`

`U = 1.4 \ Percent = 0.014 \\`

`n = 3 \\`

`\text{The probability of disrupton}, P(n ) = S + (1 – S) U^(n) \\`

`= 0.0023 + (1 – 0.0023)(0.014)^(3) \\`

`= 0.0023 + 0.9977(0.000002744) \\`

`= 0.0023 + 0.000002 \\`

`= 0.0023 \\`

Therefore, the probability that all three suppliers will disrupt = 0.0023