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Conditional Probability of Metropolitan School Systems

1.) a metropolitan school system consists of two districts- north and south. the north district contains 60% of all students, and the south district contains 40% of all students. a minimum competency test was given to all students. 10% of the north district students failed, and 15% of the south district students failed.

What is the probability that a student who has failed the test came from the south district?

a.) 0.15
b.) 0.40
c.) 0.50
d.) 0.75

2.) a metropolitan school system consists of two districts- north and south. the north district contains 60% of all students, and the south district contains 40% of all students. a minimum competency test was given to all students. 10% of the north district students failed, and 15% of the south district students failed.

What is the probability that a student from the entire school system, chosen at random, has passed? (carry your calculations to two decimal places)

a.) 0.80
b.) 0.85
c.) 0.88
d.) 0.90

Solution Preview

These problems are easy to work out if you use examples. For these scenarios, let's say that there were 100 students total in the entire school system. Therefore, there would be 60 students in the north district (60% of 100 is 60) and 40 students in the south (40% of 100 is 40).

Since we know that 10% of the north district students failed, we can determine that 6 students failed (10% of 60 is 6). Therefore, 54 students passed (60 - ...

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