Answer to Question #191077 in Civil and Environmental Engineering for Joshua

Question

In a certain school, 40% of graduating students choose engineering courses, 35% choose medical courses and 15% choose philosophy courses and 10% are undecided. If you randomly select 15 graduating students, what is the probability that 4 choose engineering, 6 choose medical, 3 choose philosophy and the remaining are undecided?

Answer 1

Solution:

Notations-

E - Students choose engineering courses

M - Students choose medical courses

P - Students choose philosophy

U - Students choose none(undecided)

Given, $P(E)=40\%,P(M)=35\%,P(P)=15\%,P(U)=10\%$

Required probability$=^{15}C_4(0.4)^4(0.6)^{11}+^{15}C_6(0.35)^6(0.65)^{9}+^{15}C_3(0.15)^4(0.85)^{12}\\+^{15}C_2(0.1)^2(0.9)^{13}$

$\approx0.62$