# What is the probability that the next letter they draw is a letter found only in Claire's name?

## Claire, Madeline, and James each write the letters of their names on pieces of paper, with one letter on each piece. All the pieces of paper are put into a bag, and they draw one out. The first letter they draw is an "e", and they put it aside.

$\frac{2}{18} = \frac{1}{9}$

#### Explanation:

Let's first list out the letters in question:

$\left(\begin{matrix}\text{ & "Claire" & "Madeline" & "James" \\ "a" & 1 & 1 & 1 \\ "c" & 1 & 0 & 0 \\ "d" & 0 & 1 & 0 \\ "e" & 1 & 2 & 1 \\ "i" & 1 & 1 & 0 \\ "j" & 0 & 0 & 1 \\ "l" & 1 & 1 & 0 \\ "m" & 0 & 1 & 1 \\ "n" & 0 & 1 & 0 \\ "r" & 1 & 0 & 0 \\ "s} & 0 & 0 & 1\end{matrix}\right)$

And so to start, we have 3 a, 1 c, 1 d, 4 e, 2 i, 1 j, 2 l, 2 m, 1 n, 1 r, 1 s.

An e is drawn and set aside, leaving: 3 a, 1 c, 1 d, 3 e, 2 i, 1 j, 2 l, 2 m, 1 n, 1 r, 1 s.

Of the remaining 18 letters, only 2 are unique to Claire's name (1 c, 1 r). This means that the probability of drawing a letter that is unique to Claire's name is:

$\frac{2}{18} = \frac{1}{9}$