Animal greetings probability
There's a room full of elephants, and giraffes. They keep greeting each other randomly, whether or not they're the same species.
How many total animals are there if:
-
If a giraffe has a 1 in 12 chance to greet an elephant.
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An elephant has a 1 in 14 chance to greet another elephant.
Image: <a href="https://www.freepik.com/free-vector/african-animals-cartoon_1021455.htm">Designed by Freepik</a>
The answer is 85.
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1 solution
If we let E represent the number of elephants, and G represents the number of Giraffes, we can construct these two equations off the conditions.
1 2 1 = G + E − 1 E . This is the number of elephants over the number of other animals in the room
1 4 1 = G + E − 1 E − 1 . This is the number of other elephants over the number of other animals in the room.
Rearranging both equations for G + E − 1 , we get:
G + E − 1 = 1 2 1 E
and
G + E − 1 = 1 4 1 E − 1
Setting them equal:
1 2 1 E = 1 4 1 E − 1
1 2 E = 1 4 ( E − 1 )
E = 7
Plugging this back into one of the first equations, we get G = 78, thus E+G= 85