Determine the number X for the given table.
Suppose that men and women are distributed in the freshman and sophomore classes of a college according to the proportions listed in the following table.
|
Class Gender
|
M
|
W
|
Totals
|
|
F
|
4
|
6
|
10
|
|
S
|
6
|
X
|
6 + x
|
|
Totals
|
10
|
6+x
|
16+x
|
A student is chosen at random and let M,W,F, and S be the events, respectively, that the student is a man, a woman, a freshman, or a sophomore. Then, being a man or a woman and being a freshman or a sophomore are independent, if
P(M ∩ F) = P(M) P(S), P(W∩ F) = P(W)P(F),
P(M∩S) = P(M) P(S), P(W∩S) = P(W)P(S).
Determine the number x so that the preceding independence relations hold.