document.write( "Question 1088806: A card is drawn from a full deck of 52 cards. What is the probability that the card is either a queen or a red card? \r
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document.write( "--I got 4/52 that a queen is drawn, and 26/52 that a red card is drawn. Would the final answer be 30/52? or am I completely lost.... \n" );
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Algebra.Com's Answer #703140 by jim_thompson5910(35256)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Define Events \n" ); document.write( "Q = card is a queen \n" ); document.write( "R = card is red (diamonds or hearts)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "P(Q) = probability that you draw a queen \n" ); document.write( "P(Q) = (number of queens)/(number of cards total) \n" ); document.write( "P(Q) = 4/52 \n" ); document.write( "P(Q) = 1/13\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "P(R) = probability that you draw a red card \n" ); document.write( "P(Q) = (number of red cards)/(number of cards total) \n" ); document.write( "P(R) = 26/52 \n" ); document.write( "P(R) = 1/2\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "-------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "P(Q and R) = probability you pick a queen AND a red card \n" ); document.write( "P(Q and R) = probability you pick a red queen \n" ); document.write( "P(Q and R) = P(Q)*P(R) ... works because Q and R are independent events \n" ); document.write( "P(Q and R) = (1/13)*(1/2) \n" ); document.write( "P(Q and R) = (1*1)/(13*2) \n" ); document.write( "P(Q and R) = 1/26\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Note: An alternative is to write it out like this \n" ); document.write( "P(Q and R) = (number of red queens)/(number of cards total) \n" ); document.write( "P(Q and R) = 2/52 \n" ); document.write( "P(Q and R) = 1/26\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "P(Q or R) = probability of queen OR a red card (or both, i.e. a red queen) \n" ); document.write( "P(Q or R) = P(Q) + P(R) - P(Q and R) see note below \n" ); document.write( "P(Q or R) = (1/13) + (1/2) - (1/26) \n" ); document.write( "P(Q or R) = (2/26) + (13/26) - (1/26) \n" ); document.write( "P(Q or R) = (2+13-1)/26 \n" ); document.write( "P(Q or R) = 14/26 \n" ); document.write( "P(Q or R) = 7/13\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Note: You are adding correctly (when you add 4/52 to 26/52); however, you forgot to subtract off the value 1/26. Why is this subtraction done? To correct for double counting. There is overlap between Q and R: namely the 2 red queens. We count each of those red queens twice when we compute P(Q)+P(R). This is why we subtract off P(Q and R) to correct for this overcounting.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "------------------------------ \n" ); document.write( "------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The answer as a fraction is 7/13 \n" ); document.write( "I have reduced the fraction as much as possible.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "If you want the answer in decimal form then use a calculator to say 7/13 = 0.53846 \n" ); document.write( "which is approximate (it converts to roughly 53.846%)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |