A space shuttle is made up of 774 "criticality 1" items. Each "criticality 1" item must have 99.99% reliability, according to standards, meaning that the probability of failure for such an item is 0.0001. Determine the probability that a. none of the "criticality 1" items would fail. b. at least one "criticality 1" item would fail.

Question

Roderick Matthews

Mathematics

15 August, 04:27

A space shuttle is made up of 774 "criticality 1" items. Each "criticality 1" item must have 99.99% reliability, according to standards, meaning that the probability of failure for such an item is 0.0001. Determine the probability that a. none of the "criticality 1" items would fail. b. at least one "criticality 1" item would fail.

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Lowe · Answer 1

a) 0.9999

b) 0.0001

Step-by-step explanation:

Given that probability of failure is 0.0001

Then;

a) finding the probability that none of the "criticality 1" items would fail will be;

1-0.0001 = 0.9999

b) To find the probability of an event occurring at least once it will be the complement of the probability of the event never occurring.

P (at least one) = 1 - P (none)

=1-0.9999 = 0.0001