Question

In: Statistics and Probability

A batch of 30 laptops contains 4 defective laptops. A sample of 4 is drawn at...

A batch of 30 laptops contains 4 defective laptops. A sample of 4 is drawn at random. What is the probability of finding 2 and just 2 defective laptops in the selected sample?

a. Less than 25%

b. More than 50%

c. Between 35% and 40%

d. Between 40% and 45%

e. Between 45% and 50%

f. Between 30% and 35%

g. Between 25% and 30%

Expert Solution

A batch of 30 laptops contains 4 defective laptops. A sample of 4 is drawn at random. We have to find the probability of finding 2 and just 2 defective laptops in the selected sample.

We can chose the sample of 4 laptops among the batch of 30 laptops in ways.

Again the sample of 4 laptops can contain 2 and just 2 defective laptops in ways.

So, the remaining (30-4) = 26 laptops will contain the other (4-2) = 2 defective laptops in ways.

For each of the ways of selecting 2 and just 2 defective laptops the other 2 defective laptops can be selected in ways.

hence , we calculate the required probability:

As, we can see the probability of finding 2 and just 2 defective laptops in the selected sample is 0.07115. i.e, approximately 7%.

ANSWER : ( option A ) the probability of finding 2 and just 2 defective laptops in the selected sample is less than 25%

orchestra answered 1 year ago

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