Answer to Question #124337 in Statistics and Probability for Yasini

Question

Employees of a certain firm receive annual reviews. In a certain department, 4 employees received excellent ratings, 15 received good ratings and 1 received marginal rating. If 3 employees in this department are randomly selected to complete a form for internal study of firm, find the probability that
(I)all 3 selected were excellent
(II)one of each category were selected

Answer 1

we are given 4 excellent,15 good and i marginal.let p(e) be probability of excellent rating = 4/20 = 1/5, p(G) be probability of good rating = 15/20 =3/4 and p(m)is the probability of marginal rating =1/20.remember there is no replacement after first and second picks

(i) probability of all 3 selected were excellent = p(E)*p(E)*p(E) without replacement

= 4/20*3/19*2/18= 1/285 = 0.0035

(ii) probability of one in each category each is given =p(E)*p(G)* P(M) without replacement

=4/20*15/19*1/18 = 1/114 = 0.0088