Question

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.
Answer:
different given events
P(A|D) equals 2/10
P(D|A) equals 2/8

Answer 1

Answer:

P(A|D) and P(D|A) from the table above are not equal because P(A|D) = $\frac{2}{10}$ and P(D|A) = $\frac{2}{8}$

Step-by-step explanation:

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

.

P(A|D) is called the "Conditional Probability" of A given D

P(D|A) is called the "Conditional Probability" of D given A

The formula for conditional probability of P(A|D) = P(D∩A)/P(D)

The formula for conditional probability of P(D|A) = P(A∩D)/P(A)

The table

               ↓         ↓       ↓

            :  C     :   D    : Total

→ A      :  6     :    2    :   8

→ B      :  1      :    8    :   9

→Total :  7     :    10  :  17

∵ P(A|D) = P(D∩A)/P(D)

∵ P(D∩A) = 2 ⇒ the common of D and A

- P(D) means total of column D

∵ P(D) = 10

∴ P(A|D) = $\frac{2}{10}$

∵ P(D|A) = P(A∩D)/P(A)

∵ P(A∩D) = 2 ⇒ the common of A and D

- P(A) means total of row A

∵ P(A) = 8

∴ P(D|A) = $\frac{2}{8}$

∵ P(A|D) = $\frac{2}{10}$

∵ P(D|A) = $\frac{2}{8}$

∵  $\frac{2}{10}$ ≠  $\frac{2}{8}$

∴ P(A|D) and P(D|A) from the table above are not equal

Answer 2

Answer: P(A|D) and P(D|A) have different given events, P(A|D) equals 2/10 and P(D|A) equals 2/8

Step-by-step explanation: The two conditional probabilities have different given events (event D and event A). The first probability has event D which gives it 2/10 as its probability. The second probability has event A which gives it 2/8 as its probability. This is why they are not equal.