Skip to main content
OlympiadHQ

Browse · harp

Print

smc

counting and probability intermediate

Problem

Each integer through is written on a separate slip of paper and all nine slips are put into a hat. Jack picks one of these slips at random and puts it back. Then Jill picks a slip at random. Which digit is most likely to be the units digit of the sum of Jack's integer and Jill's integer?
(A)
(B)
(C)
(D)
Solution
We can draw a sample space diagram, and find that of the possibilities, of them give a sum of , and each other sum mod (from to ) is given by of the possibilities (and indeed we can check that ). Thus is the most likely, so the answer is .
Final answer
A