# Resolved: Probability-The Intersection of Two Sets - Quiz

Any explanation for the above answer? I guess it should be Queens and Spades

Hey Aman,

Thank you for your question and engagement with the Probability course!

Let me first outline the purpose of the task, so that we are on the same footing. Let's say we have to sets - A and B - and let B be the smaller of the two. Among the answers, we are seeking for a pair of sets whose intersection gives the smaller set, or in other words:

A intersected with B = B

In the case of the third answer, we have the set of all the Queens in a deck (Q), which includes the Queen of Spades among other *Queens*. We also have the set of Spades (S), which is the larger of the two sets and includes the Queen of Spades, among other *Spades*. Their intersection returns a set with only one item - the Queen of Spades (QS):

Q intersected with S = QS

Set Q is not equal to set QS, therefore this answer is ruled out.

Now, let us examine the first option that is marked as correct. The first set (B) consists of all the black cards in the deck - 26 in total. The second set (C) consists of all the clubs in the deck - 13 in total - which all fall into the set of black cards. Therefore:

B intersected with C = C

which is what the task is asking for.

Hope this helps!

Kind regards,

365 Hristina

Thanks Hristina,

I understood your solution however I found the question could have beenn phrased in a better way.

Anyway, thanks a lot for this detailed explanation.