There are 2 taxi companies. Company A has 40% of German cars and company B has 10% of German cars. All other cars are Korean. Taxi aggregator assigns orders to A or B with probabilities 1/3 and 2/3 respectively. If German car arrives, what's the probability that it's from company B?
So my solution for this problem would be using Bayes Theorem
According to me the question is asking to find P(car being from company B|Being German)
So using Bayes theorem it would be equal to
$P(B|G)=(P(B) * P(G|B))/P(G)$ and that would be
$P(B|G)=((2/3)*0.1)/0.25= 4/15$ which is wrong. I would like to know where am i making mistake
Here P(B) is probability of car being from company B
P(G) is probability of car being German
I found P(G) considering there are 100 cars in both company A and B so $50/200=1/4=0.25$
Best Answer
Law of total probability:
$P(G) = P(G|A)P(A) + P(G|B) P(B) = 0.4*1/3 + 0.1*2/3 = 0.2$.
By the way, the cars should be Mercedes Benz please.