Question

In a department there are two Professors, four Readers and 6 Lecturers. A committee of three persons is to be formed out of the staff of the department. The probability that the committee consists of at least two lecturers is

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{8}$

Answer 1

Answer: (C)

$\frac{1}{2}$

1st possiblity $:0L,3R$ or $0L,2R,1P$ or $0L,1R,2P$
$P(0$\ lecturers$)=C(4,3)+C(4,2)\ast C(2,1)+C(4,1)\ast C(2,2)/C(12,3)=20/220$
2nd possibility $:$
$1L,2R,0P1L,1R,1P1L,2P,0R$
$P(1$ lecturer$)=C(4,2)\ast C(6,1)+C(4,1)\ast C(6,1)\ast C(2,1)+C(6,1)\ast C(2,2)/C(12,3)=90/220$
$\Rightarrow P=1-110/220=1/2$