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) = 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.


Now,








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


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