which value for r in the table would most likely indicate an association between the conditional…

which value for r in the table would most likely indicate an association between the conditional variables?\n0.09\n0.10\n0.13\n0.79\n\na b c total\nd 0.12 0.78 0.10 1.0\ne r s t 1.0\ntotal u x y 1.0
Answer
Explanation:
Step1: Recall independence condition
If the variables are independent, the joint - probabilities follow the rule (P(A\cap D)=P(A)\times P(D)). In a two - way table, if there is no association (i.e., variables are independent), the relative frequencies in corresponding cells should be similar. Here, (P(D) = 1.0), (P(A)) (if we assume independence) should be such that the values in the table follow a certain pattern. If the variables are independent, the proportion of (A) within (D) and (E) should be similar. Since (P(A|D)=0.12), if there is no association, (P(A|E)) should be close to (0.12).
Step2: Analyze the options
If (R = 0.09), it is relatively far from (0.12) compared to (0.10) and (0.13). A value of (R = 0.79) is extremely different from (0.12). Among the given options, a value that is most different from (0.12) would most likely indicate an association. The value (0.79) is very different from (0.12), suggesting that the distribution of (A) is different between (D) and (E), which implies an association between the conditional variables.
Answer:
0.79