Answer:
Option: A is the correct answer.
A. P(A | C) = 0.16, P(A) = 0.16, the events are independent
Step-by-step explanation:
We know that two events A and B are said to be independent if:
[tex]P(A|B)=P(A)[/tex]
(
Since, we know that if A and B are two independent events then
[tex]P(A\Bigcap B)=P(A)\cdot P(B)------------(1)[/tex]
and:
[tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]
and hence using property (1) we get:
[tex]P(A|B)=P(A)[/tex] )
from the given table we have:
[tex]P(A|C)=\dfrac{P(A\bigcap C)}{P(C)}\\\\\\P(A|C)=\dfrac{0.12}{0.75}\\\\\\P(A|C)=0.16[/tex]
and also, P(A)=0.16
As P(A|C)=P(A)
Hence, events A and C are independent.
Also we may observe that:
[tex]P(C|A)=P(C)[/tex]
(
Since, from table we have:
P(C)=0.75
and
[tex]P(C|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\P(C|A)=\dfrac{0.12}{0.16}\\\\P(C|A)=0.75[/tex] )
Hence, events A and C are independent.
