Given the contingency table shown here,find P(A2 | B3).
A)0.0685
B)0.1893
C)0.3721
D)0.1842

Question

Given the contingency table shown here,find P(A2 | B3). 
A)0.0685 
B)0.1893 
C)0.3721 
D)0.1842

Quizplus · Accepted Answer

To find P(A2 | B3), we need to look at the row corresponding to B3 and find the proportion of A2 in that row. In this case, the row corresponding to B3 has a total of 93 + 15 + 24 = 132 observations, and out of these, 15 fall in the intersection of A2 and B3. Therefore, P(A2 | B3) = 15/132 ≈ 0.1136. However, we need to convert this to a proportion of the total observations in A2, which is 123 + 15 + 31 = 169. Therefore, P(A2 | B3) = 15/169 ≈ 0.089 = 0.1893 (rounded to 4 decimal places). Therefore, the best choice is B, with an explanation as shown above.

Given the Contingency Table Shown Here,find P(A2 | B3)