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 3 suppliers will be disrupted at the same time at some point during the next five​ years is 0.0023.

Explanation:

The formula to compute the probability that n suppliers will be disrupted at the same time for a supply cycle is:

`P(n)=S+(1-S)\ U^(n)`

Here,

S = super event

U = unique event

n = number of suppliers.

The information provided is:

S = 0.23% = 0.0023

U = 1.4% = 0.014

n = 3

Compute the probability that all 3 suppliers will be disrupted at the same time at some point during the next five​ years as follows:

`P(n)=S+(1-S)\ U^(n)`

`P(3)=0.0023+(1-0.0023)* 0.014^(3)`

`=0.0023+0.0000027376888\\=0.0023027376888\\\approx 0.0023`

Thus, the probability that all 3 suppliers will be disrupted at the same time at some point during the next five​ years is 0.0023.