1. In proof testing of circuit boards, the probability that any particular diode

Question

1. In proof testing of circuit boards, the probability that any particular diode will fail is 0.01. Suppose a circuit board contains 200 diodes, all which are independent of one another. A board works properly only if all its diodes work.

a. How many diodes would you expect to fail, and what is the standard deviation of the number that will fail?

b. Assume boards are independent of one another. If five boards are shipped to a particular customer, how likely is it that at least four of them will work properly? (A board works properly only if all its diodes.)

Explanation / Answer

p = 0.01 n = 200

a. Expected failures = n * p = 200 * 0.01 = 2.

Standard deviation = (np(1-p)) = (2*0.99) = 1.4071.

b. Probability that all 200 diodes work = 0.99200 = 0.1340.

=> Probability that all five boards work = 0.13405.

Probability that four boards work = 5 * 0.13404 * (1 - 0.1340) = 0.0014.

=> Probability that atleast four boards work = 0.13405 + 0.0014 = 0.001443.

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