<PRE><B>Question 1201400</B>
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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.&lt;br&gt;
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.&lt;br&gt;
Then the other problem is worked in the same way.&lt;br&gt;
For both problems:  Number of ways of choosing 2 of the 52 cards: C(52,2) = 1326&lt;br&gt;
(1) P(both kings or both black)&lt;br&gt;
# of ways of getting 2 black cards: C(26,2) = 325&lt;br&gt;
# of ways of getting 2 kings: C(4,2) = 6&lt;br&gt;
# of ways of getting 2 black kings: C(2,2) = 1&lt;br&gt;
# of ways of getting 2 black cards or 2 kings: 325+6-1 = 330&lt;br&gt;
ANSWER: P(both kings or both black) = 330/1326 = 55/221&lt;br&gt;
(2) P(both face cards or both red)&lt;br&gt;
# of ways of getting 2 red cards: C(26,2) = 325&lt;br&gt;
# of ways of getting 2 face cards: C(12,2) = 66&lt;br&gt;
# of ways of getting 2 face cards both red: C(6,2) = 15&lt;br&gt;
# of ways of getting both face cards or both red: 325+66-15 = 376&lt;br&gt;
ANSWER: P(both face cards or both kings) = 376/1326 = 188/663&lt;br&gt;
Same answers as from the other tutor, by a different path.&lt;br&gt;
Neither path is better than the other; try both and find the one that &quot;works&quot; best for you.&lt;br&gt;
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