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aziamarie
 4 months ago
Best ResponseYou've already chosen the best response.0The 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?

aziamarie
 4 months ago
Best ResponseYou've already chosen the best response.0Events 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(BA) ≠ P(B). Events A and B are dependent because P(AB) ≠ P(B). Done

MrNood
 4 months ago
Best ResponseYou've already chosen the best response.1It tells you P(A AND B) First calculate whether P(A AND B) = P(A) x P(B)

ybarrap
 4 months ago
Best ResponseYou've already chosen the best response.0You can easily verify $$ P(A\cap B)=P(A)P(B) $$ But also $$ P(BA)=\cfrac{P(B\cap A)}{P(A)}=\cfrac{0.2484}{0.46}=0.54=P(B)\\ P(AB)=\cfrac{P(B\cap A)}{P(B)}=\cfrac{0.2484}{0.54}=0.46=P(B)\\ $$ Since \(P(BA)=P(B)\) and \(P(AB)=P(A)\), events A and B are \(independent\).

jahij1
 17 days ago
Best ResponseYou've already chosen the best response.0The 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?

jahij1
 17 days ago
Best ResponseYou've already chosen the best response.0If A and B are independent events, which equation must be true?

ybarrap
 16 days ago
Best ResponseYou've already chosen the best response.0If 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.
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