In a Scrabble® set there are 100 tiles, consisting of: E (12); A, I, (9); O, (8); N, R, T (6); D, L S, U (4); G (3); B, C, F, H, M, P, V, W, Y (2); J, K, Q, X, Z (1); and 2 blanks that can be used as wild cards to represent any letter.

A player is selecting tiles prior to making the first move.

If the first six tiles drawn are A, E, N, R, S, and T, what is the probability that the seventh tile will complete a 7 letter word?

Well, let's see. There are 94 tiles left in the bag. Here are the possibilities which will get you a 7-letter word:

E (11): NEAREST, EASTERN, etc.

I (9): RETAINS, RETINAS, etc.

O (8): SENATOR, TREASON

N (5): TANNERS

R (5): RANTERS, ERRANTS

D (4): STANDER (not sure if this is in the Scrabble dictionary)

L (4): RENTALS, etc.

U (4): SAUNTER, NATURES

G (3): STRANGE

B (2): BANTERS

C (2): CANTERS

M (2): MARTENS, SMARTEN

P (2): PARENTS

V (2): TAVERNS, SERVANT

W (2): WANTERS (not sure if this is in the Scrabble dictionary)

K (1): TANKERS

And then of course the 2 blanks can form any of those words.

The letters that won't get you anywhere: the 8 A's (they'll form Antares, but that's the proper name of a star so I don't think it counts), 5 T's, 3 S's, 2 F's, 2 H's, 2 Y's, J, Q, X, and Z.

So that's 68 out of 94, or 72.3%. Not a bad start!

Posted by Jyqm on 2006-02-03 11:17:11