A specific automotive part that a service station stocks in its inventory has an 8% chance of being defective. Suppose many cars come into the service station needing this part each week. What is the probability that the fourth part retrieved from stock is the first defective?

Question

Asher Pearson

Mathematics

23 February, 03:18

A specific automotive part that a service station stocks in its inventory has an 8% chance of being defective. Suppose many cars come into the service station needing this part each week. What is the probability that the fourth part retrieved from stock is the first defective?

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Ainsley Casey · Answer 1

6.23% probability that the fourth part retrieved from stock is the first defective

Step-by-step explanation:

For each part, we have that:

8% probability of being defective.

100-8 = 92% probability of not being defective.

The parts are independent of each other.

What is the probability that the fourth part retrieved from stock is the first defective?

The first three work correctly, each one with a 92% probability.

The fourth is defective, with an 8% probability.

P = 0.92*0.92*0.92*0.08 = 0.0623

6.23% probability that the fourth part retrieved from stock is the first defective