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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?

 May 14, 2020
 #1
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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 \(\frac{1}{36}+\frac{1}{36}=\boxed{\frac{1}{18}}\)

 May 14, 2020
edited by trumpstinks  Jun 12, 2020
 #2
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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 %  smiley

Guest May 14, 2020
edited by Guest  May 14, 2020
edited by Guest  May 14, 2020
 #3
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I think Guest is right and here's why:

 

B    --> 1         Probability for B, R, A, or T to be drawn is  1/9

R    --> 1              

I, I   --> 2         Probability for or L to be drawn MUST be greater!!!    It's  2/9

L, L --> 2

A     --> 1

N     --> 1

T     -->  1

total =  9                       I hope it's clear enough.  smiley

Guest May 15, 2020
edited by Guest  May 15, 2020
 #4
avatar+1135 
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 "The probability that I choose an I is 1/9, and the probability that I pick another I right after is 1/8"

 

Let me get this straight: on the 1st draw, the probability (1/9) is lesser than on the second one (1/8) ?!?!

 

surprise

Dragan  May 16, 2020

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