I am going over some GRE based questions and its been a while since I worked with probability. This is one of the questions
30% of Advisors have average client size b/w $500K and 1 million dollars. 34% of Advisors have average client size b/w 1 million dollars and 5 million Suppose a complete list of advisors is available and 18 are randomly selected from the list.
1)What is the expected no. of advisors that have an average client size b/w 500,000 and 1 million and and what is the expected no. of advisors that have an average client size b/w 1 million and 5 million
I am getting confused by random selection. Arent we supposed to get a total count (total no of Advisors in this case) and then get a probability.
You should look up the definition of expected value. A random selection is expected to have the same distribution as the whole, so $30\%$ of the selection is expected to be between $0.5$M and $1$M. The expected value is a long term average, so it need not be an integer.