You can use the formula for conditional probability as Puzzling did. However in this problem it is easier just to restrict yourself and enumerate the cases that are left.
<span>There are 4 jacks. One of them is a heart. So the probability is 1/4. </span>
<span>If you want to look at what the formula for conditional probability does, it adjusts your probability by restricting the "universe". </span>
<span>P(heart and jack)/P(jack) </span> <span>= (1/52)/(4/52) = 1/4</span>
The answer is no, because the Rank Theorem tells us that rank A + dim Nul A = 12 . Since the rank can be at most 10, the null space has to have dimension at least two.
