Question

Seven women are chosen for a group date on The Bachelor. The pool of women to choose from consists of 8 yoga instructors, 9 professional organizers, 10 VIP cocktail waitresses, and 3 aspiring dolphin trainers. Find the probability that:

(a) 3 yoga instructors, 2 professional organizers, 1 cocktail waitresses, and 1 aspiring dolphin trainer are chosen;

(b) at least 2 yoga instructors are chosen;

(c) all of the seven women have the same profession;

(d) either exactly 3 yoga instructors or exactly 3 professional organizers are chosen.

Answer 1

a) probability that 3 yoga instructors, 2 professional organizers, 1 cocktail waitresses, and 1 aspiring dolphin trainer are chosen = =56*36*10*3/2035800 =0.0297

b)

P( at least 2 yoga instructors are chosen) =1-P(at most 1 has been chosen)

=1- =1-(0.0838+0.2932)=0.6230

c)P(all of the seven women have the same profession)

=P(all 7 are yoga instructors+all 7 are professional organizers+all 7 are cocktail waitresses)

= =0.00008 ~ 0.0001

d) probability =

P( exactly 3 yoga instructors)+P(exactly 3 professional organizers)-P(3 from both)

=

=0.2012+0.2469-0.0300 =0.4181