Counting

Alex chooses a number at random from the set {1, 2, 3, 4, 5}.  Winnie also chooses a number at random from the same set.  (They can choose the same number.)  What is the probability that the product of their numbers is at least 4?    

There are 25 combinations possible.    

20 of them multiply to 4 or more:     1,4  1,5    

                                                         2,2  2,3  2,4  2,5    

                                                         3,2  3,3  3,4  3,5     

                                                         4,1  4,2  4,3  4,4  4,5     

                                                         5,1  5,2  5.3  5,4  5,5    

Therefore the probability is 20 / 25 or 80%.    

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