Question

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

Answer 1

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.

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.