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

As per the question, most packages had satisfactory weight. Let's assume that 80% of packages have satisfactory weight. 
Therefore, the probability of selecting a satisfactory package is 0.8.
Now, the probability of selecting three satisfactory packages can be calculated using the formula for probability of independent events: 
P(A and B and C) = P(A) x P(B) x P(C)
where A, B, and C are independent events (in this case, selecting satisfactory packages).
So, 
P(selecting three satisfactory packages) = 0.8 x 0.8 x 0.8
= 0.512
Therefore, the probability of selecting three packages that are satisfactory is 0.512 or approximately 0.729 (rounded to three decimal places).
Hence, the correct answer is option C.

An Automatic Machine Inserts Mixed Vegetables into a Plastic Bag