Question

A and B are two events. Let P(A) = 0.3, P(B) = 0.9, and P(Aand B) = 0.24. Which statement is true?

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Answer 1

blue one (c), not independent because P(A|B) ≠ P(A)

Explanation:

Two events are independent of each other if you can mulitply them to get their intersection

To find the conditonal probability of two independent events you can use the following idea/formula

P(A|B)= (P(A)*P(B))/P(B) which simplifies to P(A) (so the probability of A given B when A and B are independent of each other is just the probability of A)

Now with the numbers we're given let's find P(A|B)

.24/.9= .26666666666667

Because this is not equal to .3 (or P(A)) the answer must be the blue one