Three groups announce a one-day convention to be held in June. What is the probability that at least two organizations choose the same day for their convention?

June has 30 days

1st group can have choice of any day.
prob = 1
prob that 2nd group is different from the first = 29/30
prop that 3 groups are different = 1 x 29/30 x 28/30

prob that at least 1 picked the same day
= 1 - (1)(29/30)(28/30)
= 22/225
= appr .0977

(For a problem similar to yours you might want to google "birthday paradox" )