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?

Answer 1

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" )