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?
Solution
The combination of AENRST forms seven letter words with 18 other letters. They are (with number of tiles remaining) :- B2; C2; D4; E11; G3; H2; I9; K1; L4; M2; N5; O8; P2; R5; T5; U4; V2; W2.
In addition there are 2 blanks that may be used as wild cards.
Total 75.
There are 94 tiles remaining
79.7872% of the tiles allow a 7 letter word to be formed
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