Question

Without consultation with each other, each of 4 organizations announces a 1-day convention to be held during June. Find the probability that at least two organizations specify the same for their convention.

Answer 1

I'm getting 1/3

Answer 2

and I'll show you how i modeled it

Answer 3

can you explain how you got that?

Answer 4

the answer is 47/250 apparently

Answer 5

Imagine that the orgs are ordered as #1, 2, 3, and 4. Neither of them know what the others have picked, but #1 picks first, #2 second and so on.

When #1 picks, she picks 1 day out of 30.
When #2 picks, she has 1 shot out of 30 for picking the same day as #1
When #3 picks, either, 1 and 2 are on the same day, in which case we don't even have to record any more OR 1 and 2 are on different days and the odds of #3 picking the same day as either #1 or #2 is 2 out of 30
Finally when #4 picks, she has 3 chances out of 30 for choosing the same day as one of the other 3 orgs.
Now we add everything up and get 1/30 + 2/30 + 3/30 + 4/30
= 1/3

Answer 6

I see, i thought you said two or more, but the question is asking for "at least two"

Answer 7

I think we can use the same line of reasoning.

Answer 8

okay thanks

Answer 9

A very stubborn question.
You can make a tree with orgs #1 - #4
Then look for symmetry in the tree to get a few simple fractions that add to get 47/250