A quality control engineer inspects a random sample of 3 calculators from a lot of 20 calculators. If such a lot contains 4 slightly defective calculators, what is the probability that the inspector's sample will contain (1) no slightly defective calculators, (2) one slightly defective calculators,(3) at least two slightly defective calculators.
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Answer:
0.512
0.128
0.04
Step-by-step explanation:
Total calculator = 20
slightly defective calculators = 4
Probability of selecting slightly defective calculator = 4/20 = 1/5 = 0.2
Probability of not selecting slightly defective calculator = 1 -0.2 = 0.8
Sample picked = 3
probability that the inspector's sample will contain
(1) no slightly defective calculators = all non defective calculator
= (0.8)³ = 0.512
(2) one slightly defective calculators = one defective + 2 non defective
= 0.2 (0.8)² = 0.128
(3) at least two slightly defective calculators = 2 defective or 3 defective
= (0.2)²(0.8) + (0.2)³
= 0.032 + 0.008
= 0.04
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