Dating Service Discussion
Description
Scenario
THE DATING SERVICE, HEARTS AND DIAMONDS, SPECIALIZES IN MATCHING PEOPLE WHO ENJOY ENTERTAINMENT VENUES. THE COMPANY HAS A NUMBER OF COUNTING PROBLEMS INVOLVED WITH THEIR BUSINESS MODEL.
As part of the client intake process, clients are asked to answer eighty “yes/no questions,” twenty “values” questions where the answers ranged from 1 – 10, a question asking the client to rank eight “hard choices” ordinally, that is, by first, second, third, etc., and a free-form question about ten “likes and dislikes.”
Assume that every client has a 60% chance of answering each “yes/no” question with a “yes,” and that the answer to each “yes/no” question is independent of every other answer to the other “yes/no” questions.
Instructions
Based on the information given above, answer the following questions.
What is the probability that two different clients will have the same answer to question #2?
What is the expected number of “yes” answers to “yes/no” questions?
WHAT IS THE PROBABILITY THAT A CLIENT SELECTS AT MOST 40 “YES” ANSWERS TO “YES/NO” QUESTIONS?
What is the probability of exactly 50 “yes” answers to “yes/no” questions?
What is the probability that the hard choice, “I am late to work,” is ranked #1 and the hard choice, “I get no coffee this week,” is ranked #8 if all rankings are equally likely?
What is the probability that Barbara, Carl, Georg, and Henrietta are randomly chosen from a set of twenty clients for a four-person group date if all possible choices are equally likely?
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