Question

Johnson Chemicals is considering two options for its supplier portfolio. Option 1 uses two local suppliers. Each has a "unique-event" risk of 4.5%, and the probability of a "super-event" that would disable both at the same time is estimated to be 1.3%. Option 2 uses two suppliers located in different countries. Each has a "unique-event" risk of 14%, and the probability of a "super-event" that would disable both at the same time is estimated to be 0.27%. a) The probability that both suppliers will be disrupted using option 1 is _ (round your response to five decimal places) b) The probability that both suppliers will be disrupted using option 2 is ___ (round your response to five decimal places) c) Which option would provide the lowest risk of a total shutdown? Option 1 or Option 2?

          Johnson Chemicals is considering two options for its supplier portfolio. Option 1 uses two local suppliers. Each has a "unique-event" risk of 4.5%, and the probability of a "super-event" that would disable both at the same time is estimated to be 1.3%. Option 2 uses two suppliers located in different countries. Each has a "unique-event" risk of 14%, and the probability of a "super-event" that would disable both at the same time is estimated to be 0.27%.

a) The probability that both suppliers will be disrupted using option 1 is _______ (round your response to five decimal places)
b) The probability that both suppliers will be disrupted using option 2 is _________ (round your response to five decimal places)
c) Which option would provide the lowest risk of a total shutdown? Option 1 or Option 2?

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Added by Dustin H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jacob Fry

03/06/2023

Step 1

The probability of both suppliers being disrupted due to unique events is the product of their individual unique-event risks: 0.045 * 0.045 = 0.002025. Now, we need to add the super-event risk, which is 0.013. So, the total probability of both suppliers being Show more…

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Johnson Chemicals is considering two options for its supplier portfolio. Option 1 uses two local suppliers. Each has a "unique-event" risk of 4.5%, and the probability of a "super-event" that would disable both at the same time is estimated to be 1.3%. Option 2 uses two suppliers located in different countries. Each has a "unique-event" risk of 14%, and the probability of a "super-event" that would disable both at the same time is estimated to be 0.27%. a) The probability that both suppliers will be disrupted using option 1 is _______ (round your response to five decimal places) b) The probability that both suppliers will be disrupted using option 2 is _________ (round your response to five decimal places) c) Which option would provide the lowest risk of a total shutdown? Option 1 or Option 2?

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00:01 So in this question we have two options.

00:05 So option one, we have that the probability of a supplier going down due to a unique event is 4 .5%.

00:19 And the probability of both suppliers going down due to a super event is 1 .3%.

00:31 Option two, the probability of a unique event happening to each of the suppliers is 14%.

00:39 But the probability of a super event happening to both suppliers at the same time is 0 .27%.

00:49 So first of all, what's the probability that both suppliers will be disrupted using option 1? so probability both disrupted in option 1 is going to be the probability that a unique event happens to both.

01:01 So the probability of a unique event in option 1 squared plus the probability that a super event happens.

01:13 So plus the probability of a super event happening.

01:16 But then we have to take away the probability that a unique event happens to both and the super event happens because that's counted twice.

01:24 Because this counts over the super event happening or not happening.

01:30 This counts over the unique events happening or not happening.

01:35 So this is super in one.

01:40 But then we have to take away the probability of unique in one.

01:46 In 1 squared times the probability that a super event happens in 1.

01:54 This assumes that they're all independent, so they do need to be independent for this analysis to work.

02:01 So what is this? so this is going to be 0 .045 squared plus 0 .013, minus 0 .45 squared times 0 .013, which is 1 .50%...

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