Problem # 3: A box consists of 12 components, 7 of which are defective. (a) Comp

Question

Problem # 3: A box consists of 12 components, 7 of which are defective. (a) Components are selected and tested one at a time, without replacement, until a non-defective component is found. Let X be the number of tests required. Find P(X= 6). (b) Components are selected and tested, one at a time without replacement, until two consecutive non defective components are obtained. Let X be the number of tests required. Find P(X = 5). Problem #3(a): 0.04545 Problem #3(b): 0.265151 Just Save Submit Problem #3 for Grading Problem #3 | Attempt #1 Attempt #2 Attempt #3 Your Answer: 3(a) 0.20433 3(a) 0.04545 3(a) 3(b) 0.39731682 3(b) 0.265151 3(b) 3(a) 0/1x 3(a) 3(b) 0/1x3(b) Your Mark: 3(a) 0/1x 3(b) 0/1x

Explanation / Answer

a) P(X =6 ) is computed as:

= Probability that the first 5 selected are defective * Probability that the 6th one is defective

= ( 7c5 / 12c5 ) * ( 5 / 7)

= 0.0189

Therefore 0.0189 is the required probability here.

b) P(X=5) is possible in the following cases: Let D represent Defective and N represent Non defective

Therefore the required probability here is : 0.0265 + 0.0442 + 0.0265 = 0.0972

Therefore 0.0972 is the required probability here.

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