Probability - Taxi Question The probability of hiring a taxi from garage A, B and C is $0.3$, $0.5$ and $0.2$ respectively. The probability that the taxi ordered will be late from A is $0.07$, from B is $0.1$ and from C is $0.2$. (i) Illustrate this information on a tree diagram showing the probability on all branches. I have attempted this part of the questions and the tree diagram is attached in the link. (ii) A garage is chosen at random, determine the probability that a) the taxi will arrive late I have attempted this as well: $$P (\text{Taxi arriving late}) = 0.07 + 0.1 + 0.2 = 0.37$$ Is this correct? b) the taxi will come from Garage C given that it is late. I'm not sure how to work this one. !enter image description here

No, your answer to (a) is not correct. You want to find $$\begin{align}P(\text{taxi late})&=P(\text{taxi late}|A)P(A)+P(\text{taxi late}|B)P(B)+P(\text{taxi late}|C)P(C)\\\&=(0.07\times0.3)+(0.1\times0.5)+(0.2\times0.2)\\\&=\cdots\end{align}$$Here we used the law of total probability.

Hint for (b): $$P(C|\text{taxi late})=\frac{P(\text{taxi late}\cap C)}{P(\text{taxi late})}=\frac{0.2\times0.2}{\text{answer from part (a)}}$$ This is the definition of conditional probability.