A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.

0.292

Step-by-step explanation:

When we select the first widget, there are 20 good widgets from 25 total.

When we select the second widget, there are 19 good widgets from 24 total.

So on and so forth.

So the probability is:

P = (20/25) (19/24) (18/23) (17/22) (16/21)

P = 0.292

Alternatively, we can calculate this using combinations.

We are selecting 5 widgets from a total of 25. ₂₅C₅

From the 5 defective widgets, we want to select 0. ₅C₀

From the 20 non-defective widgets, we want to select 5. ₂₀C₅

So the probability is:

P = (₅C₀ ₂₀C₅) / ₂₅C₅

P = 0.292