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In a batch of 44 shafts, there are 7 shafts that do not meet the length specific

ID: 3131239 • Letter: I

Question

In a batch of 44 shafts, there are 7 shafts that do not meet the length specifications. A sample of 4 shafts are selected at random (without replacement) and inspected.
-What is the probability that there are at least two shafts in the sample that do not meet the length specifications?
(Need step-by-step help with this problem) In a batch of 44 shafts, there are 7 shafts that do not meet the length specifications. A sample of 4 shafts are selected at random (without replacement) and inspected.
-What is the probability that there are at least two shafts in the sample that do not meet the length specifications?
(Need step-by-step help with this problem)
-What is the probability that there are at least two shafts in the sample that do not meet the length specifications?
(Need step-by-step help with this problem)

Explanation / Answer

Total number of shafts = 44

Defected Shafts = 7

Shafts selected at random = 4

P(At least two defected shafts) = 1 - [P(no defected shaft) + P(1 defected shaft)]

P(no defected shaft) = 37C4 / 44C4

= 0.4865

P(1 defected shaft) = (7/44)*(37/43)*(36/42)*(35/41)

= 0.1002

P(At least two defected shafts) = 1-[0.4864+0.1002]

= 0.4133