# Resolved: Quiz Question - Independent Events - card example

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

Didnt get it :(

Hey Pedro,

Thank you for reaching out!

Could you please specify which element of the explanation you found confusing? I will do my best to clarify.

Kind regards,

365 Hristina

Do you mean that in order for the conditions to be able to apply for P(A|B) then there must be an intersection of a completely overlap?