C2 It is thought that there are 1200 moose in the Yellowston

C2: It is thought that there are 1200 moose in the Yellowstone Park moose population. Last year 75 moose were captured and tagged. Six months later 300 moose are captured. Define the RV, X, to be the number of tagged moose in the group of 300 most recently captured moose. We will assume that all moose are still living and that the population total has not changed. a. Name the probability distribution that can be appropriately used to find probabilities of X. b. What is the probability that 20 of the most recently captured moose are tagged? C3: During the 2013-20 14 regular season, Brian Roberts of the Charlotte Hornets had a free throw shooting percentage was 0.940. a. What is the probability that the first free throw he manages to hit is on his fourth attempt? b. On average, how many free throws will Roberts have to take before he makes one?

Solution

(C2)(a) X follows Binomial(n=300, p=75/1200=0.0625)

P(X=x)=300Cx*(0.0625^x)*(1-0.0625)^(300-x), for x=0,1,2,...,300

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(b) So the probability is

P(X=20) = 300C20*(0.0625^20)*(1-0.0625)^(300-20)

=0.08803272

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(C3)(a) The probability is

(1-0.94)^3*0.94 = 0.00020304

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(b)1/0.94=1.06383