Question

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.

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)