Question

a machine has 0.04 probability of producing a defective item. If it produces 6 items find:
a. probability none is defective
b. at least one is defective
c. all are defective

Answer 1

Use a binomial probability formula or use a binomial probability table.

Formula:

P(x) = (nCx)(p^x)[q^(n-x)]

For a): Find P(0) for none
For b): Take 1 - P(0) for at least 1
For c): Find P(6) for all

If you use the table, p = .04, n = 6 (sample size), x = the values needed for a, b, c.

(Note: q in the formula is 1-p).

I hope this will help get you started.

Answer 2

0.76