Question 367943
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The probability of anything is the number of outcomes you consider to be a success divided by the total number of outcomes.  You want to draw a single card from a standard 52-card deck.  That means there are 52 possible outcomes -- and we already have the denominator of our fraction.  There are 13 spades in the deck and there are 3 face cards per suit and 4 suits, so there are 12 face cards.  But 3 of those 12 face cards are spades which we already counted when we counted the 13 spades.  So we have 13 spades plus 9 face cards that are not spades for a total of 22 possible sucessful draws.


P(Spade or Face) = *[tex \Large \frac{22}{52}\ =\ \frac{11}{26}]


Just a touch over 42%.


If the odds in favor are *[tex \Large m:n], then the probability is *[tex \Large \frac{m}{m\ +\ n}]


For your problem then, the probability was *[tex \Large \frac{11}{26}\ =\ \frac{11}{11\ +\ 15}], hence the odds in favor are *[tex \Large 11:15]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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