Answer to Question #190666 in Statistics and Probability for Sampada

Question

A committee of four has to be formed from among 3 economist 4 engineer and statistician and a doctor

1) what is the probability that each of the four professional is repeated on the committee

2)what is the probability that the committee consist of doctor and at least one economist

Answer 1

Total number of profession = 3+4+1+1=9

Number of ways in which we select 4 profession $= ^9C_4=126$

(1) Probability that each of the four professional is repeated on the committee-

$=\dfrac{ ^3C_1\times ^4C_1\times 1\times 1}{126}=\dfrac{12}{126}=\dfrac{2}{21}=0.0952$

(2) Probability that the committee consist of doctor and at least one economist-

$=\dfrac{1\times ^3C_1\times ^7C_2+1\times ^3C_2\times ^7C_1+1\times ^3C_3}{126}=\dfrac{63+21+1}{126}=\dfrac{85}{126}=0.6746$