Answer to Question #144824 in Statistics and Probability for Cameron Foster

Question

Play Arts is launching a new line of Final Fantasy Seven figurines in celebration of Final Fantasy 7
Remake. The marketing team sent out an e-mail survey to Square Enix fans and discovered 40% of
respondents were Final Fantasy fans; 35% of respondents were Kingdom Hearts fans; and the rest were
Tomb Raider fans. 95% of Final Fantasy fans would purchase the figurines; 85% of Kingdom Hearts
fans would purchase the figurines; and 80% of Tomb Raider fans would purchase the figurines. Please
keep solutions exact to four decimal places.

(a) Show the information using the tree diagram Do not convert decimals to fractions
(b) P(Final Fantasy Fan | Fan would purchase the figurine)
(c) P(Kingdom Hearts fan | Fan would not purchase the figurine.

Answer 1

a)

b)P(final fantasy fan | fan would purchase the figurine)

$P(F. F|P) =[P(P|F. F) *P(F. F)] /[P(P|F. F) *P(F. F) +P(P|K. H) *P(K. H) +P(P|T. R) *P(T. R)] =(0.95*0.4)/(0.95*0.4+0.85*0.35+0.8*0.25) =0.4330$

c) P(K. H|N. P) =1-P(K.H|P)

$P(K. H|P) =[P(P|K. H) *P(K. H)] /[P(P|K.H) *P(K. H) +P(P|F. F) *P(F. F) +P(P|T.R)*P(T.R)] =(0.85*0.35)/(0.85*0.35+0.95*0.4+0.8*0.25)=0.3390$

P(K. H|N. P) =1-0.3390=0.6610