Using the below table:     A1 A2 B1 0.4 0.3 B2 0.2 0.1   Calculate P(A1 | B2). Calculate P(A2 | B1). Are the events independent? Explain. Please do not solve using Microsoft Excel.  My professor is not teaching through excel and I would like to see the steps and equation for purposes of studying for my exam.

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.