Question

Your quality control lab needs 10 quartz cuvettes and from past experience, you know each cuvette you order has a 10% chance of being flawed. How many cuvettes will you need to order to be 98% sure of getting at least 10 good cuvettes?

Answer 1

There is a 10% chance of being flawed.

=> For every 'x' cuvettes taken, there is a chance of '0.1x' cuvettes to be flawed and '0.9x' cuvettes to be good.

=> To ensure that '0.9x' cuvettes are good, we need to order 'x' cuvettes.

=> To ensure that 'x' cuvettes are good, we need to order x / 0.9 = ' 10x / 9 ' cuvettes.

But this is of 100% surety.

For being 98% sure that 'x' cuvettes will be good, we need to order 0.98 * 10x / 9 = 9.8x / 9 cuvettes.

Here, x = 10

=> To be 98% sure of getting at least 10 good cuvettes, we need to order 9.8 * 10 / 9 = 98 / 9 = 10.888888 cuvettes.