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\n" ); document.write( "I personally find it easier to count the numbers of ways of getting the desired results and then calculating the probability, rather than working with probabilities to do all the calculations.
\n" ); document.write( "In counting the number of ways of getting the desired results, we use the inclusion-exclusion principle. For example, in the first problem where the desired outcome is 2 kings or 2 face cards, we count the number of ways of getting 2 kings, add the number of ways of getting 2 black cards, and then subtract the number of ways we counted twice -- the ways that get 2 cards that are BOTH black AND kings.
\n" ); document.write( "Then the other problem is worked in the same way.
\n" ); document.write( "For both problems: Number of ways of choosing 2 of the 52 cards: C(52,2) = 1326
\n" ); document.write( "(1) P(both kings or both black)
\n" ); document.write( "# of ways of getting 2 black cards: C(26,2) = 325
\n" ); document.write( "# of ways of getting 2 kings: C(4,2) = 6
\n" ); document.write( "# of ways of getting 2 black kings: C(2,2) = 1
\n" ); document.write( "# of ways of getting 2 black cards or 2 kings: 325+6-1 = 330
\n" ); document.write( "ANSWER: P(both kings or both black) = 330/1326 = 55/221
\n" ); document.write( "(2) P(both face cards or both red)
\n" ); document.write( "# of ways of getting 2 red cards: C(26,2) = 325
\n" ); document.write( "# of ways of getting 2 face cards: C(12,2) = 66
\n" ); document.write( "# of ways of getting 2 face cards both red: C(6,2) = 15
\n" ); document.write( "# of ways of getting both face cards or both red: 325+66-15 = 376
\n" ); document.write( "ANSWER: P(both face cards or both kings) = 376/1326 = 188/663
\n" ); document.write( "Same answers as from the other tutor, by a different path.
\n" ); document.write( "Neither path is better than the other; try both and find the one that \"works\" best for you.
\n" ); document.write( " \n" ); document.write( "