Question

Suppose there is indeed a 2% failure rate among all syringes. If you check 20 syringes chosen at random from among all syringes, what is the chance that you find at least 1 faulty syringe? (You may assume that syringes are chosen with replacement from a population in which 2% of syringes are faulty.)

Answer 1

To find the chance of finding at least 1 faulty syringe, we can calculate the probability of not finding any faulty syringe and subtract it from 1.

Step-by-step explanation:

To find the chance of finding at least 1 faulty syringe, we can calculate the probability of not finding any faulty syringe and subtract it from 1.

Since the failure rate is 2%, the probability of finding a faulty syringe in one trial is 0.02. Therefore, the probability of not finding a faulty syringe in one trial is 1 - 0.02 = 0.98.

Since the syringes are chosen with replacement, the probability of not finding a faulty syringe in 20 trials is (0.98)^20. Therefore, the probability of finding at least 1 faulty syringe is 1 - (0.98)^20 ≈ 0.33244 or 33.244%.

Answer 2

The chance that you find at least 1 faulty syringe is 0.4%.

Step-by-step explanation:

If we suppose that 2% of the population is faulty, we can say that 2 of 100 are faulty.

We use cross multiplication to get this chance of find at least 1 faulty if we check 20 syringes.

100----0.02

20 -----?

?= (20 x 0.02)/100=0.004

That means 0.4%