SOLUTION: Two cards are chosen from a standard deck of 52 cards without replacement. Determine the probability that at least one of the cards is a spade. please show work, thanks

Algebra ->  Probability-and-statistics -> SOLUTION: Two cards are chosen from a standard deck of 52 cards without replacement. Determine the probability that at least one of the cards is a spade. please show work, thanks      Log On


   

Question 329482: Two cards are chosen from a standard deck of 52 cards without replacement. Determine the probability that at least one of the cards is a spade. please show work, thanks
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at 3 possibilities:
First card is a spade, second isn't
Second card is a spade, first isn't
Both cards are spades.
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.
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P(spade, not spade)=%2813%2F52%29%2839%2F51%29
P(not spade, spade)=%2839%2F52%29%2813%2F51%29
P(spade,spade)=%2813%2F52%29%2812%2F51%29
P(at least one spade)=P(spade,not spade)+P(not spade,spade)+P{spade,spade)
P(at least one spade)=1170%2F2652=585%2F1326=0.441