A survey finds customers are charged incorrectly for 1 out of every 10 items. Suppose a customer purchases 13 items. Find the probability that the customer is charged correctly on atleast 3 items

Answer 1

Prob( 3 or more) = 1 - Prob(2) - Prob(1) - Prob(0)

Prob(2) = (13 choose 2) ( 0.9)^2 (0.1)^11 = (13*12/2) * 0.9^2 (0.1)^11 = 78*0.81*(-11)

= 6.318 * 10^(-10)

Prob(1) = (13 choose 1)( 0.9)(0.1)^12 = 13 * 0.9 * 10^(-12) = 1.17 * 10^(-12)

Prob(0) = (13 choose 0)(0.9)^0 (0.1)^13 = 1 * 1 * 10^(-13) = 10^(-13)

99.9999999999%