Two non-zero digits x and y were randomly (uniform distribution) generated by a computer.
I. What is the probability that x-y is a multiple of 4 ?
Ii. Same question for 5 instead of 4.
1 2 3 4 5 6 7 8 9
+---+---+---+---+---+---+---+---+---+
1 +4 5+ + + + 4 + 5 + + + 4 +
+---+---+---+---+---+---+---+---+---+
2 + +4 5+ + + + 4 + 5 + + +
+---+---+---+---+---+---+---+---+---+
3 + + +4 5+ + + + 4 + 5 + +
+---+---+---+---+---+---+---+---+---+
4 + + + +4 5+ + + + 4 + 5 +
+---+---+---+---+---+---+---+---+---+
5 + 4 + + + +4 5+ + + + 4 +
+---+---+---+---+---+---+---+---+---+
6 + 5 + 4 + + + +4 5+ + + +
+---+---+---+---+---+---+---+---+---+
7 + + 5 + 4 + + + +4 5+ + +
+---+---+---+---+---+---+---+---+---+
8 + + + 5 + 4 + + + +4 5+ +
+---+---+---+---+---+---+---+---+---+
9 + 4 + + + 5 + 4 + + + +4 5+
+---+---+---+---+---+---+---+---+---+
There are 81 equally likely outcomes.
21 have a difference that's a multiple of 4 for a probability of 7/27 ~= 0.259259259259259.
17 have a difference that's a multiple of 5 for a probability of 17/81 ~= 0.209876543209877.
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Posted by Charlie
on 2022-03-28 11:32:12 |
presented graphically
