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# The letters in the word MATHEMATICIAN are written out in the following

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Math Expert
Joined: 02 Sep 2009
Posts: 60518
The letters in the word MATHEMATICIAN are written out in the following  [#permalink]

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02 Dec 2019, 00:25
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73% (01:42) correct 27% (02:25) wrong based on 11 sessions

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The letters in the word MATHEMATICIAN are written out in the following sequence: MAATTTHHHH…. so that the nth letter of the word is repeated n times. If a letter is selected at random from this sequence, what is the probability that it is an ‘A’?

A. $$\frac{3}{91}$$

B. $$\frac{23}{91}$$

C. $$\frac{3}{13}$$

D. $$\frac{5}{13}$$

E. $$\frac{31}{91}$$

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The letters in the word MATHEMATICIAN are written out in the following  [#permalink]

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02 Dec 2019, 00:32
Explanation:

MATHEMATICIAN has 3 A’s: one in the 2nd position, one in the 7th position, and one in the 12th position.
That means in this sequence there will be 2+7+12=21 A’s.
The total number of letters in the sequence is 1+2+3+…+13. This is an arithmetic series.
The sum of an arithmetic series can be determined by taking the average of the first and last terms and multiplying this by the number of terms: S={(1+13)*13}/2
=7*13 = 91.
So 21 out of 91 letters are A’s, so the probability of selecting an A is 21/91 = 3/13.
IMO-C

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The letters in the word MATHEMATICIAN are written out in the following   [#permalink] 02 Dec 2019, 00:32
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