A box contains 25 transistors of which 7 are defective. A transistor is selected
ID: 2922335 • Letter: A
Question
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
a) As there are a total of 7 defective transistors, the number of non defective transistors is computed as: = 25 - 7 =18
Therefore the average number of transistors tested or the expected number of transistors tested before getting a non defective transistor is computed as:
= Total number of transistors / Total number of non defective transistors
= 25/18
= 1.3889
Therefore the expected number of transistors tested would be 1.3889
b) Now as the expected number of transistors tested is 1.3889 out of which 0.3889 is the defective one tested and 1 is the non defective one, therefore the expected amount of time they would spend in the entire quality control examination is computed as:
= 0.3889*2 + 1*1
= 1.7778 hours
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