MATH 314 Quiz 19

Please submit a Jupyter notebook to the following repository by today at 4.00pm with your solution(s) to the problem(s) below. https://classroom.github.com/a/w6NSzqH-

1. Suppose Romeo and Juliet are going to meet somewhere between 8.00 and 8.59 (60 minutes). Each will arrive uniformly across the 60 minutes and stay for exactly 15 minutes. What is the probability that they meet? From yesterday in class, the answer is $0.425$.
   1. Write Python code to calculate (no random numbers) this probability, without using the fraction we developed in class yesterday.
   2. Write Python code to estimate (generate random numbers) this probability.
2. Consider the following survey in which $250$ people who recently purchased a car were asked whether or not they bought a new or used car and whether or not they were satisfied with their purchase.

   	satisfied	not satisfied
   new car	92	28
   used car	83	47

   1. What is the probability that a person bought a new car?
   2. What is the probability that a person is satisfied with their car purchase?
   3. What is the probability that a person bought a new car and is satisfied?
   4. What is the probability that a person is satisfied given the person bought a used car?
   5. What is the probability that a person is unsatisfied given the person bought a new car?