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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 :

Answer:

The probability that all three suppliers will disrupt = 0.0023

Step-by-step explanation:

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

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

[tex]S = Super \ event \\[/tex]

[tex]U = Unique \ event \\[/tex]

[tex]L = Loss \\[/tex]

[tex]S = 0.23 \ Percent = 0.0023 \\[/tex]

[tex]U = 1.4 \ Percent = 0.014 \\[/tex]

[tex]n = 3 \\[/tex]

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

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

[tex]= 0.0023 + 0.9977(0.000002744) \\[/tex]

[tex]= 0.0023 + 0.000002 \\[/tex]

[tex]= 0.0023 \\[/tex]

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

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