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 satisfactory?
Click on the arrows to vote for the correct answer
A. B. C. D. E.C
P(all three satisfactory) = 0.9*0.9*0.9 = 0.729.
To calculate the probability of selecting and finding that all three packages are satisfactory, we need to multiply the probabilities of each package being satisfactory.
Given that most packages have a satisfactory weight, we know that the probability of selecting a satisfactory package is 90%.
Since three packages are selected, we can assume that the selections are independent events. This means that the probability of selecting three satisfactory packages in a row is equal to multiplying the probability of selecting a satisfactory package each time.
So, the probability of selecting and finding that the first package is satisfactory is 0.90 (or 90%). The probability of selecting and finding that the second package is satisfactory, assuming the first package was satisfactory, is also 0.90. Similarly, the probability of selecting and finding that the third package is satisfactory, assuming the first two packages were satisfactory, is also 0.90.
To find the probability of all three events occurring, we multiply the probabilities together:
0.90 * 0.90 * 0.90 = 0.729
Therefore, the probability of selecting and finding that all three packages are satisfactory is 0.729 or 72.9%.
The correct answer is C. 0.729.