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Two distinct numbers are selected simultaneously and at random from the set \(\{1, 2, 3, 4\}\) What is the probability that the smaller one divides the larger one? Express your answer as a common fraction.

 Feb 6, 2022
 #1
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There are a total of 4 choose 2 = 6 pairs that can be chosen. This number is small enough to go through each pair one by one.

 

(1, 2), (1, 3), (1, 4): one divides into every number, so all of these work

(2, 3): 2 does not divide evenly into 3

(2, 4): 2 divides evenly into 4

(3, 4): 3 does not divide evenly into 4

 

This gives 4 pairs that work for an overall probability of 4/6 = 2/3.

 Feb 6, 2022

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