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Conditionally equally Likely
Let \(A\) and \(B\) be two events with positive probability. When does \(\mathbf{P}(A|B)=\mathbf{P}(B|A)\) ?
Random Letters
Suppose a word is picked at random from this sentence. Find:
- the outcome space for this random experiment
- the chance the word has at least 4 letters;
- the chance that the word contains at least 2 vowels (a,e,i,o,u)
- the chance that the word contains at least 4 letters and at least 2 vowels.
- What is the distribution of the length of the word picked ?
- What is the distribution of the number of vowels in the word ?
(Based on [Pitman p.9 #2 and p. 31 #6)
