Q. A box contains 15 transistors, 5 of which are defective. An inspector takes out one transistor at random, examines it for defects and replaces it. After it has replaced another inspector does the same thing and then so does a third inspector. The probability that atleast one of the inspectors finds a defective transistor, is equal to
A) 1/27
B) 8/27
C) 19/27
D) 26/27
Explanation
(c)
Probability of defective transistor $= \frac{5}{15} = \frac{1}{3}$ and probability of non-defective transistor $= 1 - \frac{1}{3} = \frac{2}{3}$
Probability that the inspectors finds non-defective transistors
$= \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{8}{27}$
Hence, probability that atleast one of the inspectors finds a defective transistor
$= 1 - \frac{8}{27} = \frac{19}{27}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.