Hi, I find it difficult to understand why the correct answer to the question about independent sets is: "Drawing a Diamond and drawing an Ace.". I hope you can help me understand where I am going wrong with this. As I understand it, the probabilities for both events must be equal, P(A) = P(B), to say that they are independent. Meanwhile, when we draw a Diamond, it influences the probability of drawing an Ace, since we might draw an Ace of Diamonds, right? What am I missing?

Hello Hubert, Strictly speaking, two events A and B are independent when the following formula holds: P(A ∩ B) = P(A) * P(B). This here is the definition of when two events A and B are independent (and not necessarily that they have equal probability). Being independent means not being influenced by the other event occuring, so it is a good idea to always think of the events taking place at the same time. In the question, let A be 'drawing a Diamond' and B be 'drawing an Ace'. Calculate the probabilities: P(A ∩ B) - this is the probability of drawing one card, which is simultaneously a Diamond and an Ace. Because there is only one such card in the deck (namely, the Ace of Diamonds), the probability of that occuring is exactly 1 /52. On the other hand, knowing that P(A) = 1 / 4 and P(B) = 1 / 13, we verify that indeed events A and B are independent. Please consider the other examples in a similar manner and try to ponder why the events are not independent. Hint - let's see what happens if A is 'drawing a four' and B is 'drawing the Ace of Spades'. Now, you get P(A) = 1 / 13 and P(B) = 1 / 52, but P(A ∩ B) = 0 because you cannot possibly draw one card which is simultaneously a four and the Ace of Spades. Try the other examples on your own. Hope this helps! Best, A. The 365 Team

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Hubert Szul

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08 Oct 2021

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12 May 2021

Resolved: Quiz Question - Independent Events - card example

in Probability / Dependent and Independent Events

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Atanas Gruev

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08 Oct 2021

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Resolved: Quiz Question - Independent Events - card example

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