The items produced by a company contain 10% defective items. Show that the probability of getting 2 defective items in a sample of 8 items is .

Let p be the probability of getting defective items out of 100 items.

And according to the question, the items produced by a company contain 10% defective items.

So, p = 10%

And also, as we know p + q = 1

If p is the probability of getting defective items out of 100, then q is the probability of not getting defective items out of 100.

⇒ q = 1 – p

Let X be the number of defective items drawn out of 8 items. (Since 8 is the sample size)

Then, the probability of getting r defective items out of 8 items is given by,

P (X = r) = ^{n}C_{r}p^{r}q^{n-r}

We know that, n = 8

Put all these values in the previous equation.

Then, the probability of getting two defective items out of a sample of 8 is given by putting r = 2.

Now,

Thus, the probability of getting 2 defective items out of a sample of 8 items is .

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