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Two events are independent if the outcome of one event does not affect the outcome of the other event. One of the following statements does NOT describe independent events. Which one?

F. A coin lands heads up, then a single 6-sided die lands with a 3 face up.

G. A king is drawn from a deck of cards, then a coin lands heads up.

H. A 4 is drawn from a deck of cards, then after replacing the card, a 4 is drawn.

J. A single 6-sided die lands with a 2 face up, then after being rolled a second time, the die lands with a1 faceup.

K. A 7 is drawn from a deck of cards, then without replacing the card, a 2 is drawn.

The answer is K, but I don't think it is not a independent event, since what does drawing a 7 have to do with drawing a 2?

HypnoticBuggyWraithVirileBevy
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I think your definition of independence is a bit misleading, as it focuses completely on the outcome, not the process. In that vein it is completely understandable to say „drawing a 7 doesn’t affect drawing a 2“.

However, what dependence/independence really tries to describe is, whether the outcome of the first event changes the context to determine the probability of the second event.

Take for example the first two. As the events are taken from completely different activities (throwing dices vs throwing coins) the output of one will certainly not affect the context of the other.

In the last example this is different. Both events come from the same activity and not inserting the first card back does change the context of drawing a 2. Indeed the probability of drawing a 2 goes up to be $4/(n-1)$, which was $4/n$ before removing a 7. Hence the events are dependent.

Jonas Linssen
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