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. Then, the probability of selecting three satisfactory packages is:
0.8 x 0.8 x 0.8 = 0.512
However, the question asks for the probability of selecting three satisfactory packages out of all the packages (which includes underweight and overweight packages). We don't know the probability of selecting underweight or overweight packages, but we do know that the probability of selecting a satisfactory package is greater than the probability of selecting an underweight or overweight package. Therefore, the probability of selecting three satisfactory packages is greater than 0.512, but less than 0.9 (since not all packages are satisfactory). The closest answer choice to this range is C) 0.729.

An Automatic Machine Inserts Mixed Vegetables into a Plastic Bag