Question

In a consignment of electric lamps, 5% are defective. If a random sample of 8 lamps are inspected, what is the probability that one or more lamps are defective?

• A. 0.6633
• B. 0.3366
• C. 0.3333
• D. 0.6666

Hint:

For problems involving "at least one" defective or successful event, it is often easier to calculate the complement (the probability of none of the events occurring) and subtract it from 1.

Answer 1

The Correct Option is A

Let the probability that a lamp is defective be \( p = 0.05 \). The probability that a lamp is not defective is \( q = 1 - p = 0.95 \).
We are asked to find the probability that one or more lamps are defective, which is the complement of the event where none of the lamps are defective.
The probability that none of the 8 lamps are defective is given by:
\[ P(\text{no defective lamps}) = (q)^8 = (0.95)^8 \approx 0.6633 \] Thus, the probability that one or more lamps are defective is the complement:
\[ P(\text{one or more defective}) = 1 - P(\text{no defective lamps}) = 1 - 0.6633 = 0.3366 \]