probability

#1
Hi My name is Angela. Can anyone help me figure out how to do this problem. I don't know where to begin.

An automobile has three factories. A, B, and C. They produce 50%, 30%, and 20% respectively of a specific model of car. 10% of the cars produced in factory A are white, 38% in factory B are white, and 31% in factory C are white. A car dealer received a car of that model type. Find the probability that it is white.
 

Martingale

TS Contributor
#2
Hi My name is Angela. Can anyone help me figure out how to do this problem. I don't know where to begin.

An automobile has three factories. A, B, and C. They produce 50%, 30%, and 20% respectively of a specific model of car. 10% of the cars produced in factory A are white, 38% in factory B are white, and 31% in factory C are white. A car dealer received a car of that model type. Find the probability that it is white.
P(W)=P([W and A] or [W and B] or [W and C])

=P(W and A)+P(W and B)+P(W and C)

=P(W|A)*P(A)+P(W|B)*P(B)+P(W|C)*P(C)

.10*.50+.38*.30+.31*.20=.226