Assume that the car lot contains 20% Volvos, 30% Porches, and 50% Lincolns. Of the Volvos, 60% have 2 airbags, 40% of the Porches have 2 airbags, and 20% of the Lincolns have airbags. Furthermore, 60% of the Volvos, 40 % of the Porches, and 90% of the Lincolns are white. The property of being white is independent from having 2 airbags. You are assigned a car at random.
If the car has 2 airbags and is white, what is the probability that it is a Volvo_____________?

Question

Assume that the car lot contains 20% Volvos, 30% Porches, and 50% Lincolns.  Of the Volvos, 60% have 2 airbags, 40% of the Porches have 2 airbags, and 20% of the Lincolns have  airbags. Furthermore, 60% of the Volvos, 40 % of the Porches, and 90% of the Lincolns are white.  The property of being white is independent from having 2 airbags.  You are assigned a car at random.
If the car has 2 airbags and is white, what is the probability that it is a Volvo_____________?

dumbcow · Answer

30.69 %

anonymous · Answer

that translates to .3069 right?

dumbcow · Answer

yeah

anonymous · Answer

that wasnt right

dumbcow · Answer

ok i'll double check...is there any rounding required when you put in an answer?

anonymous · Answer

no

dumbcow · Answer

i don't see any mistakes on my end

P(airbag) = 0.34
P(white) = 0.69
P(both) = 0.2346

P(volvo and both) = 0.36*.2 = 0.072

P(V| both) = .072/.2346 = 0.3069054

anonymous · Answer

still wont work

dumbcow · Answer

oh well...hopefully someone will correct me :)

anonymous · Answer

thank you anyway this stuff has killed me
you helped me out greatly

dumbcow · Answer

np

dumbcow · Answer

update: i noticed my mistake
A= 2 airbags, W=white
V = volvo, X = porche, L = lincoln

P(AW) = P(AW|V)*P(V) + P(AW|X)*P(X) + P(AW|L)*P(L)
          = (.36*.2) + (.16*.3) +(.18*.5)
          = 0.21

P(VAW) = P(AW|V)*P(V) = .36 * .2 = 0.072

P(V |AW) = P(VAW)/P(AW) = .072/.21 = 0.34286