Respuesta :
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 A and B are independent then:
[tex]P(A|B)=P(A)\\\\\&\\\\P(B|A)=P(B)[/tex]
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:
[tex]P (F|A) = \farc{116}{170}\\\\P(A|F)=\frac{116}{1360}\\\\P(A)=\frac{170}{2468}\\\\P(F)=\frac{1360}{2468}[/tex]
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).
