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The probability of Samantha scoring an A on a geology test (event A) is 0.46, and the probability of Judith scoring an A on the same test (event B) is 0.54. The probability of both Samantha and Judith scoring an A is 0.2484. Given this information, which statement is true?
Events A and B are independent because P(A and B) = P(A) × P(B). Events Events A and B are dependent because P(A and B) = P(A) × P(B). A and B are independent because P(B|A) ≠ P(B). Events A and B are dependent because P(A|B) ≠ P(B). Done
It tells you P(A AND B) First calculate whether P(A AND B) = P(A) x P(B)
You can easily verify $$ P(A\cap B)=P(A)P(B) $$ But also $$ P(B|A)=\cfrac{P(B\cap A)}{P(A)}=\cfrac{0.2484}{0.46}=0.54=P(B)\\ P(A|B)=\cfrac{P(B\cap A)}{P(B)}=\cfrac{0.2484}{0.54}=0.46=P(B)\\ $$ Since \(P(B|A)=P(B)\) and \(P(A|B)=P(A)\), events A and B are \(independent\).
The probability of Samantha scoring an A on a geology test (event A) is 0.46, and the probability of Judith scoring an A on the same test (event B) is 0.54. The probability of both Samantha and Judith scoring an A is 0.2484. Given this information, which statement is true?
If A and B are independent events, which equation must be true?
If A and B are independent then P(A and B) = P(A) times P(B)=0.2484. This is the only thing you need to check. If P(A) times P(B) is not equal to 0.2484, then A and B are not independent. In addition (this is just comes from the 1st part), if A and B are independent, then given A, the probability of B is just the Probability of B. In otherwords, it doesn't matter that you were given A. Similarly, if A and B are independent, then given B, the probability of A is just the Probability of A. In otherwords, it doesn't matter that you were given B.