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.
Weight % of Total -
Underweight 2.5 -
Satisfactory 90.0 -
Overweight 7.5 -
Three packages are selected from the food processing line. What is the probability of selecting and finding that all three of them are underweight?
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A. B. C. D. E.D
P(all three underweight) = 0.025*0.025*0.025 = 0.0000156.
To calculate the probability of selecting and finding that all three packages are underweight, we need to use the concept of independent events.
Given the information provided, we know that the weight distribution of the packages is as follows:
Since we are selecting three packages, we need to calculate the probability of selecting an underweight package three times in a row.
The probability of selecting an underweight package on the first draw is 2.5% or 0.025. This means there is a 0.025 probability of success (selecting an underweight package) on the first draw.
Since the events are independent, the probability of selecting an underweight package on the second draw is also 0.025.
Likewise, the probability of selecting an underweight package on the third draw is 0.025.
To find the probability of all three events occurring, we multiply the individual probabilities together:
0.025 * 0.025 * 0.025 = 0.000015625
This value is equivalent to 0.0000156 when rounded to the required number of decimal places.
Therefore, the correct answer is D. 0.0000156.