Asingle card is drawn from a 52 standard deck. find the conditional probability that the card is a heart given that it's a jack.?

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. 

There are 4 jacks. One of them is a heart. So the probability is 1/4. 

If you want to look at what the formula for conditional probability does, it adjusts your probability by restricting the "universe". 

P(heart and jack)/P(jack) 
= (1/52)/(4/52) = 1/4

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