Question

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Answer: 0.595
A factory produces two different widgets, types A and B. 30% of the widgets are type A. Of the type A
widgets, 1% are defective whereas of the type B widgets, 3% are defective. If a widget is selected at
random and is found to be defective, what is the probability it is type A?

Answer 1

The probability that a randomly selected defective widget is of type A is 12.5%.

Step-by-step explanation:

The student asked about finding the probability that a randomly selected defective widget is of type A. To solve this, we can use Bayes' theorem. First, let's identify the probabilities given:

• P(A) = Probability that a widget is type A = 30% or 0.30.
• P(B) = Probability that a widget is type B = 70% or 0.70 (since there are only two types).
• P(Defective|A) = Probability that a widget is defective given it's type A = 1% or 0.01.
• P(Defective|B) = Probability that a widget is defective given it's type B = 3% or 0.03.

We need to find P(A|Defective), the probability that a randomly selected defective widget is type A. We can use the formula:

P(A|Defective) = [P(Defective|A) * P(A)] / [P(Defective|A) * P(A) + P(Defective|B) * P(B)]

Plugging in the values we get:

P(A|Defective) = [0.01 * 0.30] / [0.01 * 0.30 + 0.03 * 0.70]

P(A|Defective) = 0.003 / (0.003 + 0.021)

P(A|Defective) = 0.003 / 0.024 = 0.125

So, the probability that a randomly selected defective widget is of type A is 12.5%.