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) = nCrprqn-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.
Thus, the probability of getting 2 defective items out of a sample of 8 items is .
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