# Probability of drawing a spade and then a heart from a deck of cards

What is the probability of drawing a heart and then a spade in 2 successive draws from a standard deck of cards? Do we consider these as independent events thus yielding:

$$\Pr(\text{Spade and Heart})=\Pr(\text{Spade})\times\Pr(\text{Heart})\rightarrow\frac{13}{52}\times\frac{13}{52}$$

or conditional so that:

$$\Pr(\text{Spade then Heart})=\Pr(\text{Spade})\times\Pr(\text{Heart})\rightarrow\frac{13}{52}\times\frac{13}{51}$$

• As a friendly piece of advice, people here are more likely to help if you format your question correctly, and put the question in the body as well. See here: math.meta.stackexchange.com/questions/5020/… – The Count Jun 24 at 0:12
• I think the answer is within the phrase "successive draws". – ArsenBerk Jun 24 at 0:18

If you're wanting to draw a heart and a spade, then you could get the heart first, or the spade first. The probability of doing this with replacement is $$2(1/4)(1/4) = 1/8$$. Doing it without replacement is $$2(1/4)(13/51) = 13/102$$. (The $$2$$ out front considers heart then spade, and spade then heart.)