SOLUTION: Determine whether the following individual events are overlapping or non-overlapping. Then find the probability of the combined event. Drawing either a black six or a black three o

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Question 1173394: Determine whether the following individual events are overlapping or non-overlapping. Then find the probability of the combined event. Drawing either a black six or a black three on one draw from a regular deck of cards.
Answer by math_helper(2461) About Me  (Show Source):
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These are nonoverlapping ("independent" is more commonly used).



2 black sixes

2 black threes



P(drawing a black six of a black three on one draw) = (2+2)/52 = 4/52 = highlight%281%2F13%29



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Example of an overlapping (dependent) event:



P(drawing a ten OR drawing a red card)  ... here there is dependency because a there are 26 red cards and four tens, but two of the tens are red (i.e. two tens belong to both sets, they are in the intersection of the two sets).  The probability is   (26 + 4 - 2)/52.   Notice how the common part (intersection, the 2 red tens) has to be subtracted once, this is because it is counted in both the 26 red and 4 tens, so otherwise those two red tens would have been counted twice.  To learn more look up the inclusion-exclusion principle.