I have a set of tiles that are stamped with the letter B, R, I, L, L, I, A, N, T. If i choose two tiles at random, what is the probability that they will have the same letter on them?
+51 First post:
The two letters that appear twice in the word BRILLIANT are I and L. The probability that I choose an I is \(\frac{1}{9}\), and the probability that I pick another I right after is 1/8 (as I already picked a letter, so there is one less to pick from). So the probability of picking two I's is \(\frac{1}{9}*\frac{1}{8}=\frac{1}{72}\), and the same goes for L too, so the probability of picking the same two letters in a row is \(\frac{2}{72}=\boxed{\frac{1}{36}}\)
Edited:
The two letters that appear twice in the word BRILLIANT are I and L. The probability that I choose an I is \(\frac{2}{9}\) (2 I's to pick from) , and the probability that I pick another I right after is 1/8 (as there is only one "I" left to pick, and there are now only 8 letter to pick from). So the probability of picking two I's is \(\frac{2}{9}*\frac{1}{8}=\frac{2}{72}=\frac{1}{36}\), and the same goes for L too, so the probability of picking the same two letters in a row is \(\frac{1}{36}+\frac{1}{36}=\boxed{\frac{1}{18}}\)
Check out your answer again.
(I and I)or(L and L)
2/9 * 1/8 + 2/9 * 1/8 = 4/72 = 1/18 or 5.55 % 
