Question

A dumpling machine automatically inserts mixed vegetables and meat filled wontons into a plastic package. 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

Required:
What is the probability of selecting two packages that are satisfactory?

a. 0.900
b. 0.729
c. 0.810
d. 0.075

Answer 1

c. 0.810

Explanation:

Given, total % of satisfactory packages = 90% = 0.90

Now, since selecting a satisfactory package is independent of any other trials (i.e. all the selection trials are independent to each other)

Hence, Probability of selecting two packages that re satisfactory

P(Selecting 2 satisfactory packages) = (0.90)^2

P(Selecting 2 satisfactory packages) = 0.90*0.90

P(Selecting 2 satisfactory packages) = 0.810

Note: We are selecting product since the chance of selecting in each trials are independent.