Question

In a stat class, there are 18 juniors and 10 seniors; 6 of the seniors are females and, 12 of the juniors are males. a) Complete the following contingency table for this scenario. If a student is randomly chosen from this group: b) What is P(student is a junior)? c) What is P(student is a male and a junior)? d) What is P(student is a male or a senior)? e) What is the probability the student is a male if you know the student is a junior? f) Are the events being a junior and being a male disjoint? (You must supply a reason.) g) Are the events being a junior and being a male independent events? (You must supply a reason and show your formula used.) 11) Suppose you randomly select three students for a special assignment, selecting them one at a time. What is the probability that your first two selections are juniors and the third is a senior?

Answer 1

from above data:

	junior	senior	total
male	12	4	16
female	6	6	12
total	18	10	28

b)

P(student is a junior) =18/28=9/14

c)

What is P(student is a male and a junior) =12/28 =6/14

d)

P(student is a male or a senior) =(16+10-4)/28=22/28=11/14

e)probability the student is a male if you know the student is a junior =P(male|Junior)=12/18=2/3

f)

no as 12 common elements are there between male and junior,

g)

as P(male)=12/28=3/7 is nt equal to P(male|junior) ; therefore  being a junior and being a male are not independent events

11)

probability that your first two selections are juniors and the third is a senior

=¹⁸C₂*¹⁰C₁/²⁸C₃ =153*10/3276 =85/182