Question

The probability for event A is 0.3, the probability for event B is 0.5, and the probability of events A and B is 0.25. Are the events independent?

Answer 1

The events A and B are dependent.

Step-by-step explanation:

Two events A and B are considered independent if the probability of their intersection, P(A AND B), is equal to the product of their individual probabilities, P(A) and P(B). In this case, P(A)=0.3, P(B)=0.5, and P(A AND B)=0.25. To determine if the events are independent, we compare P(A AND B) with P(A)P(B).

If P(A AND B) = P(A)P(B), then the events are independent. If not, they are dependent.

Let's calculate:

P(A AND B) = 0.25, P(A)P(B) = (0.3)(0.5) = 0.15

Since P(A AND B) is not equal to P(A)P(B), we can conclude that the events A and B are dependent.

Answer 2

no because P(A) times P(B) is not equal to P(A AND B)

Step-by-step explanation:

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