Explain why p(a|d) and p(d|a) from the table below are not equal.

Step-by-step explanation:

Recall the definition for conditional probability.

We have P(A/D) = P(A and D)/P(D)

P(AD) = 2/17

P(A) = 8/17 and P(D) = 10/17

From the definition of conditional probability,

P(A/D) = P(AD)/P(D) = 2/17 divided by 10/17 = 1/5

But P(D/A) = P(AD)/P(A) = 2/17 divided by 8/17 = 1/4

Hence the two are not equal.

This is because there is a difference in the denominators

P(A|D) and P(D|A) from the table are not equal because the total number of A and D are not equal

From the table, we have the following parameters:

P(A|D) and P(D|A) are both conditional probabilities, and they are calculated using:

So, we have:

From the above computations, we have:

This is so, because:

The total number of A and D are not equal

Read more about probabilities at:

link