document.write( "Question 551256: How many cards must be drawn from a standard 52 card deck to be certain that 4 cards of the same suit are drawn?\r
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Algebra.Com's Answer #359566 by josmiceli(19441)![]() ![]() You can put this solution on YOUR website! The 1st 13 cards you draw could all be the \n" ); document.write( "same suit. Not likely, but possible. \n" ); document.write( "If you draw 14 cards, there is zero probability \n" ); document.write( "that they will all be the same suit, and it is certain \n" ); document.write( "you will have at least 2 cards of different suits. \n" ); document.write( "If you draw more cards until you have drawn 26, \n" ); document.write( "it is still possible you have 13 of one suit and \n" ); document.write( "13 of another suit \n" ); document.write( "If you draw one more card to make 27, you know \n" ); document.write( "that you are certain to have at least 3 cards of \n" ); document.write( "different suits. \n" ); document.write( "If you keep drawing until you have 3x13 = 39 cards \n" ); document.write( "it is still possible that you have only cards of 3 suits, \n" ); document.write( "Drawing one more card makes it 100% certain that you \n" ); document.write( "have all 4 suits \n" ); document.write( "So, you must draw 40 cards to know that you have cards \n" ); document.write( "of all 4 suits \n" ); document.write( " |