Same Birthday Project: A group of students compare their birthdays. a. What is the

Chapter 9, Problem 13

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Same Birthday Project: A group of students compare their birthdays. a. What is the probability that Shawns birthday is not the same as Marks? b. If Shawn and Mark have different birthdays, what is the probability that Friedas birthday is not the same as Shawns and not the same as Marks? c. What is the probability that Shawn and Mark have different birthdays and that Frieda has a birthday different from both of them? d. Using the pattern you observe in part c, find the probability that a group of ten students will all have different birthdays. Give a decimal approximation for the result. e. What is the probability that in a group of ten students, at least two have the same birthday (that is, not all ten have different birthdays)? f. Write a program to compute a list of probabilities that at least two people have the same birthday in a group of x people. Store the output in lists of x and P(x) for use in subsequent graphing. Use the program to make a list of P(x) for 2 through 60 people. g. Plot the graph of the probability distribution in part f. Use the data in the lists output by the program without doing further computations. Sketch the pattern followed by the points. h. From the graphical or numerical data, find out how many people must be in a group to have the probability that at least two people will have the same birthday equal to i. 50% ii. 99% Surprising?