Question

A business organization needs to make up a 6 member fund-raising committee. The organization has 10 accounting majors and 8 finance majors. What is the probability that at most 2 accounting majors are on the committee?
a) 0.0045
b) 0.2014
c) 0.1998
d) 0.0015
e) 0.0030

Answer 1

Answer:b

Step-by-step explanation:

Given

Committee  needs 6 fund raising member and

there are 10 accounting majors and 8 finance majors

Probability that at most 2 accounting majors are on the committee

There are three cases for this

i)0 accounting member and 6 finance major

ii)1 accounting member and 5 finance major

iii)2 accounting member and 4 finance major

Therefore required Probability P is

$P=\frac{^{10}C_0\times ^{8}C_6}{^{18}C_6}+\frac{^{10}C_1\times ^{8}C_5}{^{18}C_6}+\frac{^{10}C_2\times ^{8}C_4}{^{18}C_6}$

$P=\frac{28+560+3150}{18564}=0.2013$