4 (20 Points) Suppose thot a shipment of 120 electronies component contains 15 d

Question

4 (20 Points) Suppose thot a shipment of 120 electronies component contains 15 defective components. II the control engineer selects 5 of these components at random and test them for either being defective or not Sdetective Sat vondorm a. What is the probability that exactly 4 of those selected are defecti KY) 12.0 1776 b. What is the probability that fewer than 4 selected are not defective? ,3,2 4 c. What is the probability that at least 3 of those selected are defective 2. d. What is the probability that at least 2 of those selected are not defectiv )! 3)

Explanation / Answer

Solution

P(defective component) = 15/120 = 0.125

n = 5

Let X be the selected defective electronic components

X follows binomial with n = 5 and p =0.125

(a) P(x=4) = 5C4 (0.125)4(1-0.125) = 0.0011

(b) P(fewer than 4 is non defective) = 5C0(0.875)0(0.125)5 + 5C1 (0.875)(0.125)4+5C2(0.875)2(0.125)3+5C3(0.875)3(0.125)2 = 0.1207

(c)P(X>=3) = P(X=3)+P(X=4)+P(X=5)

= 5C3(0.125)3(0.875)2 + 5C4 (0.125)4(1-0.125) + 5C5(0.125)5 = 0.0163

(d) P(atleast 2 are not defective) = 1- 5C0(0.875)0(0.125)5+ 5C1(0.875)(0.125)4 = 0.9989

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