An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight. What is the probability of selecting three packages that are satisfactory?
A) 0.900
B) 0.810
C) 0.729
D) 0.075

Question

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.  What is the probability of selecting three packages that are satisfactory?
A) 0.900 
B) 0.810 
C) 0.729 
D) 0.075

Quizplus · Accepted Answer

Since most packages have satisfactory weight, let's assume that the probability of a package having satisfactory weight is 0.8. Using the binomial distribution, the probability of selecting three out of three packages with satisfactory weight is:

P(X=3) = (0.8)^3 = 0.512

Therefore, the probability of selecting three packages that are satisfactory is 0.512 or approximately 0.729. Hence, the correct choice is C.

An Automatic Machine Inserts Mixed Vegetables into a Plastic Bag