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Choose one of the words in the following sentence uniformly at random and then choose one...

Choose one of the words in the following sentence uniformly at random and then choose one of the letters of that word, again uniformly at random:

SOME DOGS ARE BROWN

Find the probability that the chosen letter is R.

Math   Statistics-And-Probability   
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Answer #1

Answer:

Given that,

Choose one of the words in the following sentence uniformly at random and then choose one of the letters of that word, again uniformly at random:

SOME DOGS ARE BROWN

The probability that the chosen letter is R:

P(R | SOME) P(SOME)+ P(R | DOGS)P(DOGS)+P(R | ARE) P( ARE) + P(R | BROWN) P(BROWN)

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