Given two events, A and B, if the probability of A is 0.7, the probability of B is 0.3, and the joint probability of A and B is 0.21, then the two events are independent?Select one:a.True.b.False.
Question
Given two events, A and B, if the probability of A is 0.7, the probability of B is 0.3, and the joint probability of A and B is 0.21, then the two events are independent?Select one:a.True.b.False.
Solution
b. False.
To determine if two events are independent, we need to check if the joint probability of A and B (P(A ∩ B)) is equal to the product of their individual probabilities (P(A) * P(B)).
In this case, P(A) = 0.7, P(B) = 0.3, and P(A ∩ B) = 0.21.
If we multiply P(A) and P(B), we get 0.7 * 0.3 = 0.21.
However, the joint probability P(A ∩ B) is also given as 0.21.
Since P(A ∩ B) = P(A) * P(B), the two events A and B are independent. Therefore, the correct answer is a. True.
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