Answer: The correct option is (1) Dependent.
Step-by-step explanation: For two events, we are given the following values of the probabilities :
P(A ∩ B) = 0.20, P(A) = 0.49 and P(B) = 0.41.
We are to check whether the events A and B are independent or dependent.
We know that
the two events C and D are said to be independent if the probabilities of their intersection is equal to the product of their probabilities.
That is, P(C ∩ D) = P(C) × P(D).
For the given two events A and B, we have
[tex]P(A)\times P(B)=0.49\times0.41=0.2009\neq P(A\cap B)=0.20\\\\\Rightarrow P(A\cap B)\neq P(A)\times P(B).[/tex]
Therefore, the probabilities of the intersection of two events A and B is NOT equal to the product of the probabilities of the two events.
Thus, the events A and B are NOT independent. They are dependent events.
Option (1) is CORRECT.
