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:
\(P(A|B)=P(A)\)
(
Since, we know that if A and B are two independent events then
\(P(A\Bigcap B)=P(A)\cdot P(B)------------(1)\)
and:
\(P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}\)
and hence using property (1) we get:
\(P(A|B)=P(A)\) )
from the given table we have:
\(P(A|C)=\dfrac{P(A\bigcap C)}{P(C)}\\\\\\P(A|C)=\dfrac{0.12}{0.75}\\\\\\P(A|C)=0.16\)
and also, P(A)=0.16
As P(A|C)=P(A)
Hence, events A and C are independent.
Also we may observe that:
\(P(C|A)=P(C)\)
(
Since, from table we have:
P(C)=0.75
and
\(P(C|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\P(C|A)=\dfrac{0.12}{0.16}\\\\P(C|A)=0.75\) )
Hence, events A and C are independent.
