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.

1 Answer

Answer:

#2/18=1/9#

Explanation:

Let's first list out the letters in question:

#(("","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))#

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:

#2/18=1/9#