Question

Which of the following can be determined about events A and C from the table.

A. P(A | C) = 0.16, P(A) = 0.16, the events are independent

B. P(A | C) = 0.16, P(C) = 0.16, the events are independent

C. P(C | A) = 0.75, P(C)=0.75 the events are not independent

D. P(C | A) = 0.75, P(A)=0.75 the events are not independent

Answer 1

Option: A is the correct answer.

A. P(A | C) = 0.16, P(A) = 0.16, the events are independent

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)=(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)=(P(A\bigcap C))/(P(C))\\\\\\P(A|C)=(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)=(P(A\bigcap B))/(P(A))\\\\\\P(C|A)=(0.12)/(0.16)\\\\P(C|A)=0.75` )

Hence, events A and C are independent.

Answer 2

The correct answer for this question is this one: "C. P(C | A) = 0.75, P(C)=0.75 the events are not independent."

The statement that can be determined about events A and C from the table is that P(C | A) = 0.75, P(C)=0.75 the events are not independent. Hope this helps answer your question.