Instruction: The following questions need you show all your work in details. 5 p

Question

Instruction: The following questions need you show all your work in details. 5 points) A machine produces defective parts with three different probabilities ( ending on its state of repair. If the machine is in good working order, it produces defective parts with probability 0.02. If it is wearing down, it produces defective parts with robability 0.1. If it needs maintenance, it produces defective parts with probability 03. The probability that the machine is in is 0 .1, and the probability that it needs maintenance is 0.1. Compute the probability down that a randomly selected part will be defective.

Explanation / Answer

Let P(G), P(W) and P(M) denotes the probability that machine is in good condition, wearing down or in maintenance respectively. So,

P(G) = 0.8, P(W) = 0.1 and P(M) = 0.1

Let P(D) be the probability to produce defective parts. So,

P(D | G) = 0.02 , P(D | W) = 0.1 , P(D | M) = 0.3

By law of total probability,

P(D) = P(D | G) P(G) + P(D | W) P(W) + P(D | M) P(M)

= 0.02 * 0.8 + 0.1 * 0.1 + 0.3 * 0.1

= 0.056

So, the probability that a randomly selected part will be defective is 0.056.

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