Symmetric Probabilities? (Corrected)
Let set be the set of all positive integers from to
Let set be the set of all positive integers whose digits are in ascending order.
When you randomly select an element from each set, with which set do you have a greater probability of having at least one 5 in the number chosen?
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1 solution
[Note: This is just a logical way I thought in order to solve the problem.]
As numbers get bigger and bigger, there is more and more 'overlap' between numbers. For example, in two-digit numbers, 55 is the only number in which a 5 was 'wasted', hence lowering the probability a little. However, in three-digit numbers, there are many, many more instances of this happening, such as 505, 550, 551....
When numbers get higher and higher, the extra 'overlap' causes the probability to drop.