Let's say we had the word STATISTICS, and it was hanging on a wall, then two letters in the word blew off, and somebody found them. What are the chances they put them in the correct order?
here is what I have.
A = letters are put in order I = letters are identical
P(A given I) = 1 P(A given I compliment) = 1/2
I want to use the total probability theorem, but I have a hard time grasping what P(I) could be, I'm sure it would be 1 / 10 NCR something, but I'm not sure what to put.
Here is a solved version of this problem.
Word = CANAL
A = words are in the right order I = words are identical
P(A given I ) = 1 P(A given I^c) = 1/2 P(I) = 1/5 choose 2
P(A) = 1*1/10 + 1/2*9/10
by the total probability theorem.