Question

In a shipment of 80 vials, only 13 do not have hairline cracks. if you randomly select 3 vials from the shipment, what is the probability that all 3 of the selected vials have hairline cracks?

Answer 1

The probability that all 3 of the selected vials have hairline cracks will be 0.583....

Step-by-step explanation

Total number of vials is 80 and 13 do not have hairline cracks.

So, the number of vials that have hairline cracks = 80-13 = 67

We need to randomly select 3 vials from the shipment. So, the total possible ways for selecting 3 vials from 80 will be:
`^8^0C_(3)`

Now, the number of ways for selecting 3 vials from 67 that have hairline cracks
`= ^6^7C_(3)`

So, the probability
`= (^6^7C_(3))/(^8^0C_(3))=0.583.....`