Resolved: Quiz Question - Independent Events - card example

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