Question

In a survey of 300 college graduates, 58% reported that they entered a profession closely related to their college major. If 6 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major?

Answer 1

If we select 6 out of 300 subjects, we can assume that the probability remains approximately constant, thus use of the binomial distribution is applicable, where
n=6
p=0.58
bin(6,0.58, 3)
=C(6,3)*0.58^3*0.42^3
=0.2891 approximately

To be more precise, we calculate the probability as:
#ways of choosing 3 out of 174 students who entered a related profession
= C(174,3)
#ways of choosing 3 out of 126 students who entered an unrelated profession
= C(126,3)
#ways of choosing 6 students out of 300
=C(300,6)
So
probability of choosing 3+3 students
= C(174,3)*C(126*3)/C(300,6)
= 0.2917

Answer 2

equation of a line

(-3,5) (-2,-6)

can you help with this exercise