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Binomial & Poisson Distributions · Question 62 of 68

What is the probability that a box of bulbs has exactly one defective bulb?

Question 62

MediumOriginal question

A factory finds that 5% of its LED bulbs are defective. They are packed in boxes of 10, and the number of defective bulbs in a box is taken to follow a Poisson distribution. (Take e−0.5=0.6065e^{-0.5} = 0.6065.)

What is the probability that a box of bulbs has exactly one defective bulb?

Options for question 62

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. P(X=1)=e−0.5(0.5)11!P(X = 1) = \frac{e^{-0.5}(0.5)^{1}}{1!}.

  2. 0.5×0.6065=0.303250.5 \times 0.6065 = 0.30325.

Worth noting

0.151625 halves again, as if 1!1! were 2.

Concept
The probability of exactly one event
Typical time
120 s
Your time
—
The rule this testsThe Poisson distribution
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