When correctly adjusted, a machine that makes widgets operates with a 5% defective rate. However, there is a 10% chance that a disgruntled employee kicks the machine, in which case the defective rate jumps up to 30%.

a) Suppose that a widget made by this machine is selected at random and is found to be defective. What is the probability that the machine had been kicked?

b) A random sample of 20 widgets was examined, 4 widgets out of these 20 are found to be defective. What is the probability that the machine had been kicked?

Hint: What is the probability of finding 4 defective widgets in a sample of 20, if (given) the machine has been kicked?

What is the probability of finding 4 defective widgets in a sample of 20, if (given) the machine has not been kicked?

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