To determine [tex]\( P(A|B) \)[/tex], the conditional probability of [tex]\( A \)[/tex] given [tex]\( B \)[/tex], we need to use the concept of independent events.
For two independent events [tex]\( A \)[/tex] and [tex]\( B \)[/tex], the occurrence of one event does not affect the occurrence of the other. This means that the probability of [tex]\( A \)[/tex] occurring given that [tex]\( B \)[/tex] has occurred ([tex]\( P(A|B) \)[/tex]) is simply the probability of [tex]\( A \)[/tex] occurring. This can be mathematically represented as:
[tex]\[ P(A|B) = P(A) \][/tex]
Given:
- [tex]\( P(A) = 0.2 \)[/tex]
- [tex]\( P(B) = 0.4 \)[/tex]
Since [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent events:
[tex]\[ P(A|B) = P(A) \][/tex]
Thus:
[tex]\[ P(A|B) = 0.2 \][/tex]
Therefore, the correct answer is [tex]\( 0.2 \)[/tex].
Thus, [tex]\( P(A|B) \)[/tex] is:
(A) [tex]\( 0.2 \)[/tex]
(B) [tex]\( 0.5 \)[/tex]
(C) [tex]\( 0.08 \)[/tex]
(D) [tex]\( 0.4 \)[/tex]
The correct choice is:
(A) [tex]\( 0.2 \)[/tex]
