Captured with Xnip 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)[3 points] 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)[3 points] What is the probability that over the year, no-one has to share the prize money? (c)[3 points] 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). NHL club (Round, draft Name Position year) Birthday Connor Bedard Forward 2022-eligible Jul 17 Xavier Bourgault Forward 2022-eligible Oct 22 Mavrik Bourque Forward Dallas (1, 2020) Jan 8 Will Cuylle Forward 2022-eligible Feb 5 Elliot Desnoyers Forward 2022-eligible Jan 21 Ridly Greig Forward Ottawa (1, 2020) Aug 8 Dylan Guenther Forward Arizona (1, 2021) Apr 10 Kent Johnson Forward Columbus (1, 2021) Oct 18 Mason McTavish Forward Anaheim (1, 2021) Jan 30 Jake Neighbours Forward St. Louis (1, 2020) Mar 29 Cole Perfetti Forward Winnipeg (1, 2020) Jan 1 Justin Sourdif Forward Florida (3, 2020) Mar 24 Logan Stankoven Forward Dallas (2, 2021) Feb 26 Shane Wright Forward 2022-eligible Apr 10 Lukas Cormier Defense Vegas (3, 2020) Mar 27 Kaiden Guhle Defense Montreal (1, 2020) Jan 18 Carson Lambos Defense Minnesota (1, 2021) Jan 14 Ryan O'Rourke Defense Minnesota (2, 2020) Apr 30 Owen Power Defense Buffalo (1, 2021) Nov 22 Donovan Sebrango Defense Detroit (3, 2020) Jan 12 Ronan Seeley Defense Carolina (7, 2020) Aug 2 Olen Zellweger Defense Anaheim (2, 2021) Sept 2