Question

The probability that a screw manufactured by a company is defective is 0.1. The company sells screws in packets containing 5 screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is .

• A. 0.41

Answer 1

The correct option is A 0.41
probability that a screw manufactured is defective;

P(d) = 0.1

$\therefore$ probability that a screw manufactured is correct;

P(c) = 1 - 0.1 = 0.9

Now the company guarantee replacement if $P(d\ge 1),$ meaning

$P(d\ge 1)=1-P(d<1)$
= 1 - P(d = 0)

$P(d\ge 1)=1-{}^5{C}_0\left(0.1{)}^0\right(0.9{)}^5$

$=1-(0.9{)}^5=0.41$