Math

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?

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  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

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  2. equation of a line

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

    can you help with this exercise

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