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Probability Level 3

Each letter in the word “ENCYCLOPEDIA” were written in 1 inch by 1 inch tiles. These tiles were put in a box. If two tiles are drawn at random without replacement, what is the probability that the two letters are the same?

\frac{1}{6}

\frac{1}{33}

\frac{1}{132}

\frac{2}{33}

1 solution

A Former Brilliant Member
Dec 27, 2016

There are 2-C’s and 2-E’s in the word. The letters that can be drawn are either 2-C or 2-E.

$P =$ $(\frac{2}{12})($ $\frac{1}{11})+($ $\frac{2}{12})($ $\frac{1}{11})$ $=$ $\frac{1}{33}$

Alternate Solution:

$P =$ $\frac{2C2 + 2C2}{12C2}$ $=$ $\frac{1}{33}$

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