Explain why P(A|D) and P(D|A) from the table below are not equal.

Answer:

The two conditional probabilities are not equal because they have different given events, which means they use different totals (denominators). P(A|D) is the probability of A given D, so it is calculated using the total for event D as the denominator: 2/10. P(D|A) is the probability of D given A, so it is calculated using the total for event A as the denominator: 2/8. Since 2/10 does not equal 2/8, the probabilities are not equal.