Defect rate of 10%

Question

Acme’s widgets have a defect rate of 10%. Find the probability that 2 widgets are broken in a 3 pack.

Acme’s widgets have a defect rate of 10%. Find the probability that 3 widgets are broken in a 15 pack

Answer 1

There are two paths that can result in 2 defectives in a 3 pack.

The first is defective or the first is good and second is defective. Each of these paths have a 10% chance. The second defective widget can follow the first path and be either the second widget in the pack or the third. If there first widget is defective the second or third can be defective. That is two 10% probability paths for a total of 20%. A 10% for first widget and 20% to get a second defective widget results in 10% times 20% or 2%.

Now if the first widget is good then there is only the path of both the second and third widgets defectives. This means the probability is 10% times 10% or 1%.

Thus the total probability of getting two defective widgets in a pack is 2% + 1% or 3%