Question

In a box of 25 external hard disks, there are 2 defectives. An inspector examines 5 of these hard disks. Find the probability that there is at least 1 defective hard disk among the 5.

Answer 1

0.3667 or 36.67%

Explanation:

The probability of getting at least 1 defective hard disk among the 5 (P(X>0)) is equal to 100% minus the probability of getting none defectives (1-P(X=0)).

If 23 out of 25 hard disks are non-defective, the probability is:

`P(X>0) = 1 -P(X=0)\\P(X>0) = 1 -(23)/(25)*(22)/(24) *(21)/(23) *(20)/(22) *(19)/(21)\\ P(X>0) = 0.3667=36.67\%`

The probability that there is at least 1 defective hard disk is 0.3667 or 36.67%.