Problem #7 A box contains 25 transistors of which 7 are defective. A transistor

Question

Problem #7 A box contains 25 transistors of which 7 are defective. A transistor is selected at random from the box and tested. If it is defective, another transistor is selected and tested; the quality control examination finishes until a nondefective transistor appears and is tested. a) What is the expected number of transistors tested? b) If the inspectors spend 1 hour every time they test a nondefective transistor and 2 hours every time they test a defective transistor, what is the expected amount of time they would spend in the entire quality control examination?

Explanation / Answer

Ans:

Number of defectives=7

Probability of defective,1-p=7/25=0.28

Probability of non defective,p=(25-7)/25=18/25=0.72

X=number of trials to get one nondefective i.e. sucess

a)Expected number of transistors tested=1/p=1/0.72=1.39

b)Expected time

if X=1,1 hr

if X=2,2+1=3 hrs

if X=3,2*2+1=5 hrs

if X=4,2*3+1=7 hrs and so on

with respective probabilities 0.72,0.28*0.72,0.282*0.72.......so on

Expected time=1.78 hrs

X P(X) time(t) P(X)*t 1 0.7200 1 0.7200 2 0.2016 3 0.6048 3 0.0564 5 0.2822 4 0.0158 7 0.1106 5 0.0044 9 0.0398 6 0.0012 11 0.0136 7 0.0003 13 0.0045 8 0.0001 15 0.0015 9 0.0000 17 0.0005 Total= 1.7776

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