Probability help

Question

Two different cards are randomly drawn from a standard deck of 52.

Let A be the event “no ♥”, and B be the event “at least one J”. Find P(A∩B).

Answer 1

P(one Jack, one non-Jack, neither is a ♥) = 3C1•36C1 ÷ 52C2 ...*

P(two Jacks, neither is a ♥) = 3C2 ÷ 52C2.

 

Compute the above two ways of satisfying this event and add their values.

 

* first nCr value corresponds to choice of one Jack, from the three that are not hearts. That leaves 36 cards from the original 39 non-hearts, excluding two other Jacks and the one Jack that was chosen.