Question

In a certain factory, Machine A makes 50% of the components, with 1 in 15 being defective. Machine B produces 25%, with 1 in 10 being defective. Machine C produces the rest, with 1 in 20 being defective.

(a) Complete the probability table for this scenario using the given template.

(b) What is the probability that a defective component is produced?

(c) If a component is selected at random and found to be defective, what is the probability it was made by Machine A?

Answer #1

a)

Defective | Not Defective | Total | |

Machine A | 0.5 | ||

Machine B | 0.25 | ||

Machine C | 0.25 | ||

Total | 0.0708 | 0.9292 |

b) the probability that a defective component is produced = 0.0708

c) If a component is selected at random and found to be defective, the probability it was made by Machine-A is a conditional probability =

The probability that the item is from Machine A given it is defective =

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