SOLUTION: Judging from recent experience, 5% of the computer keyboards produced by an automatic, high-speed machine are defective. What is the probability that out of six keyboards selected

Question 189786: Judging from recent experience, 5% of the computer keyboards produced by an automatic, high-speed machine are defective. What is the probability that out of six keyboards selected at random, exactly zero keyboards will be defective?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If there is a 5% probability that a keyboard will be defective, then there is a 95% probability that it will have no defects. So for a sample of six keyboards, whether or not any of them are defective is six independent events -- meaning that whether the first one is defective has no effect on whether any of the others are defective, and so on.

Hence, the probability that none of them will be defective is the product of the probabilities that each of them individually is not defective:

or 73.5%

Windows calculator: .95, "x^y" button, 6, "=" button.

Looking at it another way, the odds are better than 1 in 4 that one of the six will be defective.

John

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