Question

In a shipment of 62 vials, only 14 do not have hairline cracks. If you randomly select 3 vials from the shipment, what is the probability that none of the 3 vials have hairline cracks?

a) 05484
b) 0 0096
c) 00510
d) 0.4516
e) 09904
f) None of the above

Answer 1

To find the probability of none of the 3 randomly selected vials having hairline cracks, use the concept of probability and combinations.

Step-by-step explanation:

To solve this problem, we need to use the concept of probability. We have a shipment of 62 vials, where only 14 do not have hairline cracks. We want to find the probability that none of the 3 randomly selected vials have hairline cracks.

1. First, we need to determine the total number of ways of selecting 3 vials from 62. This can be done using the combination formula: C(62, 3) = 62! / (3!(62-3)!) = 496,740.
2. Next, we need to determine the total number of ways of selecting 3 vials without hairline cracks. Since there are 14 vials without hairline cracks, this can be done using the combination formula: C(14, 3) = 14! / (3!(14-3)!) = 364.
3. Finally, we can calculate the probability by dividing the number of favorable outcomes (selecting 3 vials without hairline cracks) by the total number of possible outcomes (selecting any 3 vials from the shipment): P = 364 / 496,740 ≈ 0.000733.

Therefore, the probability that none of the 3 vials have hairline cracks is approximately 0.000733. The correct option is f) None of the above.