Question

Among 40 condensers produced by a machine, 6 are defective. If we randomly check
5 condensers, what are the probabilities that
a. none are defective;
b. all are defective?

Answer 1

Answer:

40-6=34

p(e)=34/40

b. 40/40=1

Answer 2

Answer:

the probability that none of the 5 condensers checked are defective is 0.4437, and the probability that all 5 are defective is 0.00007776.

Step-by-step explanation:

To solve this problem, we can use the binomial probability formula, which calculates the probability of k successes in n independent Bernoulli trials with a probability of success p.

a. To find the probability that none of the 5 condensers checked are defective, we need to calculate the probability of success (finding a non-defective condenser) and failure (finding a defective condenser) in each trial. The probability of success is 34/40 (the number of non-defective condensers divided by the total number of condensers), and the probability of failure is 6/40. We want to find the probability of 5 successes in 5 trials, so the probability is:

P(0 successes) = (34/40)^5 = 0.4437

b. To find the probability that all 5 of the condensers checked are defective, we need to calculate the probability of failure (finding a non-defective condenser) in each trial. The probability of failure is 6/40, and we want to find the probability of 5 failures in 5 trials, so the probability is:

P(5 failures) = (6/40)^5 = 0.00007776

Therefore, the probability that none of the 5 condensers checked are defective is 0.4437, and the probability that all 5 are defective is 0.00007776.

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