In a recent year 8,073,000 male students and 10,980,000 female students were enrolled
as undergraduates. Receiving aid were 60.6% of the male students and 65.2% of the female students. Of those receiving aid, 44.8% of the males got federal aid and 50.4% of the females got federal aid. Choose 1 student at random. (Hint: Make a tree diagram.) Find the probability that the student is
A male student without aid
A male student, given that the student has aid
A female student or a student who receives federal aid
Total students
"N=8073000+10980000=19053000"
a)
"P(A|M)=0.606"
"P(\\bar{A}|M)=1-P(A|M)=1-0.606=0.394"
"P(M\\cap \\bar{A})=P(M)P(\\bar{A}|M)=\\dfrac{8073000}{19053000}(0.394)"
"\\approx0.1669"
b)
"=\\dfrac{\\dfrac{8073000}{19053000}(0.606)}{\\dfrac{8073000}{19053000}(0.606)+\\dfrac{10980000}{19053000}(0.652)}"
"=\\dfrac{8073(0.606)}{8073(0.606)+10980(0.652)}=0.4059"
c)
"P(Federal|M)=0.448(0.606)(\\dfrac{8073000}{19053000})"
"=\\dfrac{243.524736}{2117}"
"P(F\\cup Federal)=\\dfrac{1220}{2117}+\\dfrac{243.524736}{2117}"
"=\\dfrac{243.524736}{2117}=0.6913"
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