The probability that all 3 of the selected vials have hairline cracks will be 0.583....
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: [tex]^8^0C_{3}[/tex]
Now, the number of ways for selecting 3 vials from 67 that have hairline cracks [tex]= ^6^7C_{3}[/tex]
So, the probability [tex]= \frac{^6^7C_{3}}{^8^0C_{3}}=0.583.....[/tex]
