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?

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warylucknow warylucknow · Answer 1 · 2020-05-18T09:24:14+02:00

Answer:

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

Step-by-step explanation:

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

[tex]P(n)=S+(1-S)\ U^{n}[/tex]

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:

[tex]P(n)=S+(1-S)\ U^{n}[/tex]

[tex]P(3)=0.0023+(1-0.0023)\times 0.014^{3}[/tex]

[tex]=0.0023+0.0000027376888\\=0.0023027376888\\\approx 0.0023[/tex]

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.