Question

In a shipment of 58 vials, only 16 do not have hairline cracks. If you randomly select 2 vials from the shipment, what is the probability that none of the 2 vials have hairline cracks?

a) 0.5517
b) 0.4483
c) 0.0761
d) 0.0726
e) 0.9274
f) None of the above

Answer 1

To find the probability of selecting 2 vials without hairline cracks from a shipment of 58 vials, we can use the combination formula. The probability is 0.0726.

Step-by-step explanation:

To find the probability that none of the 2 vials have hairline cracks, we can use the concept of combinations. There are 58 vials in total, and only 16 do not have hairline cracks. We want to select 2 vials without hairline cracks. The number of ways to choose 2 vials without hairline cracks from the 16 available is given by the combination formula: C(16,2) = 16! / (2!(16-2)!) = 120.

The total number of ways to choose 2 vials from the 58 available is given by the combination formula: C(58,2) = 58! / (2!(58-2)!) = 1653.

Therefore, the probability is 120/1653 = 0.0726, which is option d.