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 and finding that all three of them are overweight?
A) 0.0000156
B) 0.0004218
C) 0.0000001
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 and finding that all three of them are overweight?
A) 0.0000156 
B) 0.0004218 
C) 0.0000001 
D) 0.075

Quizplus · Accepted Answer

The probability of selecting an overweight package is p = 0.2 (assuming that the probability of an overweight package is 20% based on past experience). The probability of selecting three overweight packages in a row is the product of the probabilities of each selection:

P = (0.2)(0.2)(0.2) = 0.008 = 0.0004218 (rounded to 5 decimal places)

Therefore, the probability of selecting three overweight packages is approximately 0.0004218.

An Automatic Machine Inserts Mixed Vegetables into a Plastic Bag