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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, without replacement, until a vowel is obtained. What is the expected number of letters then drawn?

Answer is 59/30. Please show each steps clearly and specifically. Thank you.

Math   Statistics-And-Probability   
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