Explain why P(A|D) and P(D|A) from the table below are not equal. A 4-column table has 3 rows. The first column has entries A, B, total. The second column is labeled C with entries 6, 1, 7. The third column is labeled D with entries 2, 8, 10. The fourth column is labeled Total with entries 8, 9, 17.

Sample Response: The two conditional probabilities are not equal because each has different given events. P(A|D) has event D as its given event, resulting in 2/10 for a probability. P(D|A) has event A as its given event, resulting in 2/8 for a probability.

Conditional probability is the probability of one event occurring  with some relationship to one or more other events

P(A|D) = 2/10

P(D|A) = 2/8

2/10  ≠  2/8

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