Events A and B have probabilities such that P(A) = 0.3, P(B) = 0.25, P(M ∪ N) = 0.425, and P(M ∩ N) = 0.075. Are events A and event B independent? (I think is the middle one)

Question options:

Yes, because P(M) - P(N) = P(M ∩ N)
Yes, because P(M) ∙ P(N) ≠ P(M ∩ N)
Yes, because P(M) ∙ P(N) = P(M ∩ N)
No, because P(M) + P(N) = P(M ∪ N)
No, because P(M) ∙ P(N) ≠ P(M ∪ N)

(C)Yes, because P(M) ∙ P(N) = P(M ∩ N)

Step-by-step explanation:

Two events A and B are independent if P(A)P(B)=P(A ∩ B)

Given events A and B such that:

P(A) = 0.3, P(B) = 0.25, P(A ∪ B) = 0.425, and P(A ∩ B) = 0.075

Since the two expression above gives the same answer, they are independent.

The correct option is C.

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .