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Two coins are tossed. If two heads are thrown, letters are chosen from the word TWOFOLD....

Two coins are tossed. If two heads are thrown, letters are chosen from the word TWOFOLD. If one head is thrown, letters are chosen from the word ONEROUS. If no heads are thrown, letters are chosen from the word NOMAD. Whichever word is used, we draw letters one at a time, the drawing to be without replacement. until a vowel is obtained. What is the expected number of letters then drawn?

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