The "Probability Appreciation Club" (PAC) meets on the first of every month and awards anyone with a birthday in the preceding month a $100 prize. However if there are two or more birthdays in that month, they have to share the prize money. (a) if my birthday is in January and there are 9 members of the club, what is the probability I will not have to share the prize money? (you can assume that each person has probability 1/12 of being born in a given month). (b) What is the probability that over the year, no-one has to share the prize money? (c) There are 22 "skaters" (forward and defence), on the roster of the 2022 Canadian World Junior Men's Hockey team. They are listed below together with their birthdays. It has been suggested that there is an unusually high probability that they are born in the first quarter of the year (that is their birth month is Jan, Feb, or March). From this data, how many are there born in these three months? What is the probability that there are 12 or more of 22 players with birth month in the first quarter of a year (assume birth months have equal probability). Name Connor Bedard Xavier Bourgault Mavrik Bourque Will Cuylle Elliot Desnoyers Ridly Greig Dylan Guenther Kent Johnson Mason McTavish Jake Neighbours Cole Perfetti Justin Sourdif Logan Stankoven Shane Wright Lukas Commier Kaiden Guhle Carson Lambos Ryan O'Rourke Owen Power Donovan Sebrango Ronan Seeley Olen Zellweger Position Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Defense Defense Defense Defense Defense Defense Defense Defense NHL club (Round, draft year) 2022 eligible 2022-eligible Dallas (1, 2020) 2022-eligible 2022-eligible Ottawa (1, 2020) Arizona (1, 2021) Columbus (1, 2021) Anaheim (1, 2021) St. Louis (1, 2020) Winnipeg (1, 2020) Florida (3, 2020) Dallas (2,2021) 2022-eligible Vegas (3, 2020) Montreal (1, 2020) Minnesota (1, 2021) Minnesota (2, 2020) Buffalo (1, 2021) Detroit (3, 2020) Carolina (7, 2020) Anaheim (2.2021) Birthday Jul 17 Oct 22 Jan 8 Feb 5 Jan 21 Aug 8 Apr 10 Oct 18 Jan 30 Mar 29 Jan 1 Mar 24 Feb 26 Apr 10 Mar 27 Jan 18 Jan 14 Apr 30 Nov 22 Jan 12 Aug 2 Sept 2

The "Probability Appreciation Club" (PAC) meets on the first of every month and awards anyone with a birthday in the preceding month a $100 prize. However if there are two or more birthdays in that month, they have to share the prize money. (a) if my birthday is in January and there are 9 members of the club, what is the probability I will not have to share the prize money? (you can assume that each person has probability 1/12 of being born in a given month). (b) What is the probability that over the year, no-one has to share the prize money? (c) There are 22 "skaters" (forward and defence), on the roster of the 2022 Canadian World Junior Men's Hockey team. They are listed below together with their birthdays. It has been suggested that there is an unusually high probability that they are born in the first quarter of the year (that is their birth month is Jan, Feb, or March). From this data, how many are there born in these three months? What is the probability that there are 12 or more of 22 players with birth month in the first quarter of a year (assume birth months have equal probability). Name Connor Bedard Xavier Bourgault Mavrik Bourque Will Cuylle Elliot Desnoyers Ridly Greig Dylan Guenther Kent Johnson Mason McTavish Jake Neighbours Cole Perfetti Justin Sourdif Logan Stankoven Shane Wright Lukas Commier Kaiden Guhle Carson Lambos Ryan O'Rourke Owen Power Donovan Sebrango Ronan Seeley Olen Zellweger Position Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Forward Defense Defense Defense Defense Defense Defense Defense Defense NHL club (Round, draft year) 2022 eligible 2022-eligible Dallas (1, 2020) 2022-eligible 2022-eligible Ottawa (1, 2020) Arizona (1, 2021) Columbus (1, 2021) Anaheim (1, 2021) St. Louis (1, 2020) Winnipeg (1, 2020) Florida (3, 2020) Dallas (2,2021) 2022-eligible Vegas (3, 2020) Montreal (1, 2020) Minnesota (1, 2021) Minnesota (2, 2020) Buffalo (1, 2021) Detroit (3, 2020) Carolina (7, 2020) Anaheim (2.2021) Birthday Jul 17 Oct 22 Jan 8 Feb 5 Jan 21 Aug 8 Apr 10 Oct 18 Jan 30 Mar 29 Jan 1 Mar 24 Feb 26 Apr 10 Mar 27 Jan 18 Jan 14 Apr 30 Nov 22 Jan 12 Aug 2 Sept 2

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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