Answer to Question #275099 in Statistics and Probability for Rose

Question

Survey of 300 households that bought large screen TVs as type of purchase and whether satisfied with the equipment produced the table below:

SATISFIED WITH PURCHASE?

TYPE OF TV Yes No Total

Plasma screen 64 16 80

Not plasma screen 176 44 220

Total 240 60 300

You are required to identify, calculate

and interpret the meaning of the following :

a. P(Plasma)

b. P(Satisfied ∩ Plasma screen)

c. P(Satisfied│Plasma screen)

d. If P(Satisfied│Plasma screen) = P(Satisfied) , what conclusion would you make?

Answer 1

P(plasma)=p(satisfied/plasma)+p(not satisfied/plasma)

a).p(plasma)=$\frac{64+16}{240} =\frac{80}{240}$

p(plasma)=$\frac{4}{15}$

b).p(satisfied n plasma screen)

p(satisfied n plasma )=$\frac{p(safisfied/p(plasma)}{p(screen)}$

from the table ,

p(satisfied n plasma screen)=$\frac{64}{300}$

P(satisfied n plasma screen)= $\frac{16}{75}$

c).p(satisfied / plasma screen)

p(satisfied / p(plasma)=$\frac{p(satisfied) n p(plasma)}{p(plasma)}$

p(satisfied)/p(plasma)=$\frac{64}{300} /\frac{80}{300}$

p(satisfied/p(plasma)=$\frac{4}{5}$

d). if p(satisfied) / p(plasma screen) = p(satisfied)

from the general probability rule we have

p(satisfied)/p(plasma screen)= $\frac{p(satisfied) n p(plasma screen)}{p(plasma screen)}$

hence its true that :

p(satisfied) / p(plasma screen) = p(satisfied)

p(satisfied)=$\frac{4}{5}$