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Probability
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If you select 3 letters (with replacement) from the word MATHEMATICAL, what is the probability of getting two 'M's.
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Bianca's G. The letters that form the word MATHEMATICS are placed in a bowl. What is the probability of choosing the letters at random so they spell the word MATHEMATICS
1 Expert Answer
There are 11 letters in MATHEMATICS which consist of 2 each of M, A and T and 1 each of H, E, I, C and S. P(M on 1st choice) = 2/11 since there are 2 M's out of 11 letters P(A on 2nd choice) = 2/10 since there are 2 A's out of 10 remaining letters P(T on 3rd choice) = 2/9 since there are 2 T's out of 9 remaining letters At this point there are 8 letters remaining which are all distinct so they must be chosen in the correct order P(C on 10th choice) = 1/2 P(S on 11th choice) = 1/1 The probability of spelling the word correctly is the product of all the probabilities P = 2*2*2 / 11! = 8 / 39916800 = 1 / 4989600 ~ 2 x 10-7
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