Question

From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random without replacement the expected number of defective items is

Answer 1

Answer:

Step-by-step explanation:

Total number of items = 10 items (Given)

Defective items = 3 items (Given)

Thus Non defective items = 10-3 = 7

Thus, out of the 10 items, 4 items can be chosen in following ways:

10C4 = (10! / 4! 6!) = 210 ways.

Let X - A  be a random variable denoting the number of defective items in a sample.

Therefore,

X = 0 (When no item is defective)-

All items chosen will be from the non-defective items. Thus -

7C4 ways = (7! / 4! 3!)

= 35 ways.

So (x = 0) = 35/210 = 1/6 .

X = 1 (When one item of the selected ones is defective and the other 3 are non-defective)-

The items need to be chosen from 3 of the 4 items from non-defective items and the remaining 1 item from the defective items. Thus -

7C3 ×3C1 = (7!/4! 3!) × (3!/2! 1!) = 35 × 3 ways

So (X=1) gives (35×2)/(210) = 1/2

Simliarly, for (X = 2): Probability = 3/10  and for (X = 3): Probability = 1/30.