Car Sounds sells and installs high-end sound systems for cars.10% of the systems that the company installs need to be re-installed because of faulty first-time installation.You plan to randomly select 20 of Car Sounds' recent installations.How likely is it that at least three of these systems will require re-installation.?
A).3230
B).3732
C).2554
D).1989 e .2868

Question

Quizplus · Accepted Answer

The probability of a system requiring re-installation is 0.1. The probability of a system not requiring re-installation is 0.9. The probability of at least three systems requiring re-installation is 1 - the probability of 0, 1, or 2 systems requiring re-installation. The probability of 0 systems requiring re-installation is 0.9^20 = 0.1216. The probability of 1 system requiring re-installation is 20 * 0.1 * 0.9^19 = 0.2189. The probability of 2 systems requiring re-installation is 20 * 19 / 2 * 0.1^2 * 0.9^18 = 0.2434. Therefore, the probability of at least three systems requiring re-installation is 1 - 0.1216 - 0.2189 - 0.2434 = 0.3230.

Car Sounds Sells and Installs High-End Sound Systems for Cars