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 overweight?
A)0.0000156
B)0.0004219
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 three packages that are overweight?
A)0.0000156 
B)0.0004219 
C)0.0000001 
D)0.075

Quizplus · Accepted Answer

Since most packages have satisfactory weight, we can assume that the probability of selecting an overweight package is low. Let p be the probability of selecting an overweight package.

Since we're selecting three packages and want all of them to be overweight, we need to multiply the probabilities:

P(three overweight packages) = p * p * p

We don't know the value of p, but we can use past experience to make an educated guess. Since some packages were overweight and some were underweight, we can assume that p is around 0.5 (i.e. there's a 50-50 chance of selecting an overweight package).

Plugging in p = 0.5, we get:

P(three overweight packages) = 0.5 * 0.5 * 0.5 = 0.125

However, the question asks for the probability in decimal form (i.e. between 0 and 1), so we need to express 0.125 in decimal form:

0.125 = 1/8 = 0.125

Therefore, the probability of selecting three packages that are overweight is 0.125, which is closest to option B: 0.0004219.

An Automatic Machine Inserts Mixed Vegetables into a Plastic Bag