Question

A and B are two events.

Let P(A)=0.3 , P(B)=0.8 , and P(A and B)=0.24 .

Which statement is true?

(A). A and B are not independent events because P(A|B)=P(A) and P(B|A)=P(B) .

(B). A and B are not independent events because P(A|B)=P(B) and P(B|A)=P(A) .

(C). A and B are independent events because P(A|B)=P(B) and P(B|A)=P(A) .

(D). A and B are not independent events because P(A|B)≠P(A) .

Answer 1

The correct answer is D because if you take P(A) or P(B) by itself you would not get P(A|B) so there is no possible way to get P(A|B) other than putting them together.

Answer 2

Answer with explanation:

For, two Events, A and B

P(A)=0.3 , P(B)=0.8 , and P(A ∩ B)=0.24

⇒P(A)×P(B)= 0.8 × 0.3= 0.24

⇒P(A ∩ B)=P(A)×P(B)

Hence the Events are Independent.

Now, by looking at the options

`P((A)/(B))=(P(A \cap B))/(P(B))=(0.24)/(0.8)=0.3=P(A)\\\\P((B)/(A))=(P(A \cap B))/(P(A))=(0.24)/(0.3)=0.8=P(B)`

The events are Independent.

None, of the option are true if the two events are independent.