SOLUTION: Consider the experiment of drawing two cards without replacement from an ordinary deck of 52 playing cards....what are the ODDS in favor of drawing a spade and a heart? This is

Question 440592: Consider the experiment of drawing two cards without replacement from an ordinary deck of 52 playing cards....what are the ODDS in favor of drawing a spade and a heart?
This is what I have: P(Spade)=13/52, P(heart without replacement)=13/51 so then I multiply and get 169/2652 reduced to 13/204. Now that is the probability of getting a heart and a spade, how to I find the odds? The formula for finding odds in favor is P(A)/1-P(A), so would my problem be set up as
(13/204) / 1-(13/204)? If thats how it is set up, how do I carry out the math? I am very confused, please help! The answer in the book is 13:91 but I can not figure out how they got there.

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The only error is that you computed the probability of drawing a spade then a heart. However, you could also draw a heart then a spade. Hence, we would double the probability to 26/204 = 13/102.

The odds of drawing a spade and heart in some order is therefore (13/102)/(1 - 13/102) = (13/102)/(91/102) = 13:91.
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