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