Question

A lot of 18 tubes have 4 defectives in them. from this lot, a total of 6 tubes are sold to a cus assume that the selections were random. what is the probability that in the six tubes sold,

none is defective?

Answer 1

The probability that none of the 6 tubes sold is defective can be calculated using the hypergeometric distribution formula.

Step-by-step explanation:

This problem is a hypergeometric problem because it involves selecting items from a finite population without replacement. The five reasons why this problem is a hypergeometric problem are:

1. The problem involves selecting 6 tubes out of a lot of 18 tubes.
2. The selection is done randomly.
3. The lot contains 4 defective tubes out of the 18.
4. Each selection affects the probability of subsequent selections because it involves sampling without replacement.
5. The probability can be calculated using the hypergeometric distribution formula.

To find the probability that none of the 6 tubes sold is defective, we can use the hypergeometric distribution formula:

P(X = 0) = (C(4,0) * C(14,6)) / C(18,6)

Where C(n,r) represents the number of combinations of choosing r items from a set of n items.