Question

A committee of three persons is to be randomly selected from a group of three men and two women and the chairperson is to be randomly selected from the committee. The probability that the committee will have exactly two women and one man, and that the chairperson will be a woman, is

• A. $\frac { 1 } { 5 }$
• B. $\frac { 8 } { 15 }$
• C. $\frac { 2 } { 3 }$
• D. $\frac { 3 } { 10 }$

Answer 1

Answer: (A)

$\frac { 1 } { 5 }$

Answer 2

n(S) = ⁵C₃ = 10

n(1) = ³C₁ . ²C₂ = 3

\P (2W and 1M) = 3/10 So, P(2W and 1M and the

chairperson is a woman)

= $\frac { 3 } { 10 }$ . $\frac { 2 } { 3 }$ = $\frac { 1 } { 5 }$ .