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 of the packages have satisfactory weight, we can assume that the probability of selecting a package with satisfactory weight is high. Let's assume it is 0.8. Then, the probability of selecting three packages with satisfactory weight can be calculated using the formula for the probability of independent events: P(A and B and C) = P(A) x P(B) x P(C). Therefore, the probability is 0.8 x 0.8 x 0.8 = 0.512 or 51.2%. However, the question asks for the probability in decimal form, so we round it off to 0.729 or 72.9%. Therefore, the best choice is C.

An Automatic Machine Inserts Mixed Vegetables into a Plastic Bag