Question

Mary begins an internship at a small company that makes touchscreens for imported smartphones. Her first assignment is to estimate the probability of rejecting a randomly sampled box of eight flat screens. But her boss explains that there are two complications. The first is that the contract between the company and the importer demands that she inspect exactly two screens per box of eight and then that she accept the box only if both screens are not defective. The second is that 60% of the boxes have only one defective screen in them while 40% of the boxes have three defective screens in them. Mary’s boss wants to know if this means that more than half the boxes will be rejected. How should Mary answer?

Answer 1

Answer:

Mary should answer that more than half of the boxes not be rejected.

Explanation:

Probability:

Box has one defective screen = 0.6

Box has three defective screen = 0.4

no. of screens in a box = 8

The box is rejected if both of the inspected screens are defective.

Probability of rejecting a box:

$=0.6\times\frac{1}{8}\times\frac{0}{7} + 0.4\times\frac{3}{8}\times\frac{2}{7}$

= 0.04286

Only 4.286% of the boxes will be rejected.

Therefore, Mary should answer that more than half of the boxes not be rejected.