Answer:
P(A|D) and P(D|A) from the table above are not equal because P(A|D) = [tex]\frac{2}{10}[/tex] and P(D|A) = [tex]\frac{2}{8}[/tex]
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) = [tex]\frac{2}{10}[/tex]
∵ 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) = [tex]\frac{2}{8}[/tex]
∵ P(A|D) = [tex]\frac{2}{10}[/tex]
∵ P(D|A) = [tex]\frac{2}{8}[/tex]
∵ [tex]\frac{2}{10}[/tex] ≠ [tex]\frac{2}{8}[/tex]
∴ P(A|D) and P(D|A) from the table above are not equal
