Solution Found!
An array of 30 LED bulbs is used in an automotive light.
Chapter 3, Problem 138E(choose chapter or problem)
An array of 30 LED bulbs is used in an automotive light. The probability that a bulb is defective is 0.001 and defective bulbs occur independently. Determine the following:
(a) Probability that an automotive light has two or more defective bulbs.
(b) Expected number of automotive lights to check to obtain one with two or more defective bulbs.
Questions & Answers
QUESTION:
An array of 30 LED bulbs is used in an automotive light. The probability that a bulb is defective is 0.001 and defective bulbs occur independently. Determine the following:
(a) Probability that an automotive light has two or more defective bulbs.
(b) Expected number of automotive lights to check to obtain one with two or more defective bulbs.
ANSWER:Step 1 of 3
Given that the number of bulbs in automotive light is \(\mathrm{n}=3\)
The probability that a bulb is defective is \(p=0.001\)
Let us denote the \(X=\text { number of defective bulbs in automotive light. }\)
\(X\) is binomial with \(\mathrm{n}=30\), \(p=0.001\).
The pmf of the binomial distribution is
\(P(X=x)=\left(\begin{array}{l} n \\ x \end{array}\right) p^{x}(1-p)^{n-x}, x=0,1,2, \ldots\)