I have a very simple question (I think). I was helping my kid with probability lessons provided on http://www.mathgoodies.com/worksheets/pdf/unit6_wks1_key.pdf. One of the questions, "What is the probability of choosing the letter i from the word probability?" has the answer 2/9 (following logic of having a sample set of 9 letters in "probability"). I contacted mathgoodies.com and suggested that if they follow that logic, then (a famous example, I guess) the probability of choosing S from MISSISSIPPI is 4/4. Which obviously isn't. Or am I confused?
Thank you
Best Answer
It depends on how they define "choosing from", I reckon, but indeed according to the natural interpretation (picking a letter uniformly at random), it should be $2/11$ The sample space is of size 9, indeed, but not all elements have equal probability:
The total is indeed $7\cdot \frac{1}{11}+2\cdot \frac{2}{11}=1$.