Question

A group of students at a high school took a standardized test. The number of students who

Answer 1

Answer: provided in the explanation section

Step-by-step explanation:

This is quite simple to analyze.

we have that:

• P (passed ) = 27/63 = 3/7

• P (passed/Underclassman ) = 15 / 35 = 3/7

• Since P (passed) = P(passed/underclassman) = 3/7

⇒ The two events are equal, hence independent.

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Answer 2

The table is attached.

Answer:

Since P(Passed) = 0.43, and P(Passed Underclassman) = 0.43, the two results are equal so these events are independent.

Step-by-step explanation:

◙ From the table, we can see the probability of students who passed will be:

$P(passed) = \frac{27}{63} = \frac{3}{7}$

Converting to decimal, we have:

P(passed) = 0.42857 ≈ 0.43

◙Probability of students who failed:

$P(failed) = \frac{36}{63} = \frac{4}{7}$

Converting to decimal, we have:

P(failed) = 0.57142 ≈ 0.57

◙ P(passed upperclassman) =

$\frac{12}{28} = \frac{3}{7}$

Converting to decimal, we have:

P(passed upperclassman) = 0.42857 ≈ 0.43

◙P(failed upperclassman) =

$\frac{16}{28} = \frac{4}{7}$

Converting to decimal, we have:

P(failed upperclassman) = 0.5714 ≈ 0.57

◙P(passed underclassman ) $= \frac{15}{35} = \frac{3}{7}$

Converting to decimal, we have:

P(passed underclassman) = 0.42857 ≈ 0.43

◙ P(failed underclassman)

$= \frac{20}{35} = \frac{4}{7}$

Converting to decimal, we have:

P(failed underclassman) = 0.5714 ≈ 0.57

Since P(Passed) = 0.43, and P(Passed Underclassman) = 0.43, the two results are equal so these events are independent.