Question

There are 11 widgets in box. 4 of them are defective and 7 of them are non-defective. Five widgets from
the box are selected at random.
a) What is the probability that exactly 2 parts will be defective, assuming no replacement after each selection?
b) What is the probability that 1 sample widget selected will be defective, assuming no replacement after each
selection?

Answer 1

x items selected from n items by ⁿC_x ways.

Where ⁿC_x = n! [ (n-x)! * x! ]

a)

Let X = number of defective parts.

P(X = 2) = ⁴C₂ * ⁷C₃ / ¹¹C₅

= 6 * 35 / 462

= 0.4545

b)

P(X = 1) = ⁴C₁ * ⁷C₄ / ¹¹C₅

= 4 * 35 / 462

= 0.3030