In: Statistics and Probability
Six names will be drawn from a group of H+2 freshmen, F+L sophomores, 2*(H-1) juniors, and 2*H seniors. Calculate (rounding your answers to three decimal places) the probability that:
a. freshmen, sophomores and juniors are equally represented. Ans.___________
b. the number of freshmen drawn equates the number of sophomores and juniors drawn. Ans.___________
c. the ratio of drawn seniors to drawn sophomores is 3:1. Ans.___________
d. the ratio of drawn juniors to drawn freshmen is at least 3:1. Ans.___
H = 6
T = 27
F = 3
L = 7
S = 47
Please do it correctly and need to show steps
Note the Number of students with their notations used in the answers are as follows...
Freshmen (F) = 8, sophomore (S0)= 10, juniors (J) =10, seniors (S1)= 12
Total number of students = 40
Part a
Possible cases are
2 freshmen, 2 sophomores,2 juniors,0 senior
1 freshman,1 sophomore,1 junior, 3 seniors
0 freshman, 0 sophomore, 0 junior, 6 seniors
Part b
Possible cases are
2 freshmen, 1 sophomore, 1 junior, 1 senior
3 freshmen,2 sophomore,1 junior, 0 senior
3 freshman, 1 sophomore,2 juniors,0 seniors
0 freshman, 0 sophomore,0 junior, 6 seniors
Part c
Possible case are as follows
0 freshmen, 1 sophomore, 2 junior, 3 senior
1 freshmen, 1 sophomore,1 junior, 3 senior
2 freshman, 1 sophomore,0 juniors,3 seniors
Part d
Possible cases are as follows
1 freshmen, 0 sophomore, 3 junior, 2 senior
1 freshmen, 2 sophomore,3 junior, 0 senior
2 freshman, 1 sophomore,3 juniors,1 senior