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kumpel [21]
3 years ago
12

We want to determine if the probability that a student enrolled in an accelerated math pathway is independent of whether the stu

dent is female. Which of the following pairs of probabilities is not a useful comparison?
a. 1360/2468 and 116/170
b. 170/2468 and 116/1360
c. 1360/2468 and 170/2468
Mathematics
1 answer:
Molodets [167]3 years ago
4 0

Answer:

The correct option is (c).

Step-by-step explanation:

The complete question is:

The data for the student enrollment at a college in Southern California is:

                    Traditional          Accelerated            Total

                  Math-pathway     Math-pathway

Female              1244                       116                   1360

Male                  1054                       54                    1108

Total                  2298                     170                  2468

We want to determine if the probability that a student enrolled in an accelerated math pathway is independent of whether the student is female. Which of the following pairs of probabilities is not a useful comparison?

a. 1360/2468 and 116/170

b. 170/2468 and 116/1360

c. 1360/2468 and 170/2468

Solution:

If two events <em>A</em> and <em>B</em> are independent then:

P(A|B)=P(A)\\\\\&\\\\P(B|A)=P(B)

In this case we need to determine whether a student enrolled in an accelerated math pathway is independent of the student being a female.

Consider the following probabilities:

P (F|A) = \farc{116}{170}\\\\P(A|F)=\frac{116}{1360}\\\\P(A)=\frac{170}{2468}\\\\P(F)=\frac{1360}{2468}

If the two events are independent then:

P (F|A) = P(F)

&

P (A|F) = P (A)

But what would not be a valid comparison is:

P (A) = P(F)

Thus, the correct option is (c).

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