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Probability Math Question?
You and your friend are playing SCRABBLE. The distribution of letters is shown below. If you pick your seven letters first, what is the probability that you will pick three vowels and four consonants? (Count Y as a vowel.)
A=9 B=2 C=2 D=4 E=12 F=2 G=3 H=2 I=9 J=1 K=1 L=4 M=2 N=6 O=8 P=2 Q=1 R=6 S=4 T=6 U=4 V=2 W=2 X=1 Y=2 Z=1 Blanks=2
1 Answer
- efqyLv 71 decade agoFavorite Answer
There are 44 vowels, 54 consonants and 2 blanks
P(no blanks) = 98/100 x 97/99 x 96/98 x 95/97 x 94/96 x 93/95 x 92/94 = 92 x 93 / (100 x 99)
P(3 vowels | no blanks) is a hypergeometric probability
http://en.wikipedia.org/wiki/Hypergeometric_distri...
In the notation on that page, N = 98, m = 44, k = 3
writing nCk for "n choose k" (since the usual notation is hard to write in ASCII text)
P(3 vowels | no blanks) = mCk (N-m)C(n-k) / NCn = 44C3 x 54C4 / 98C7
Hence the overall probability P(3 vowels, 4 consonants) = P(3 vowels|no blanks) x P(no blanks)
= 44C3 x 54C4 / 98C7 x 92 x 93 / (100 x 99)
= 0.30275 x 0.86424
= 0.2617