Q44

Consider Guwahati, $(G)$ and Delhi $(D)$ whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati has high temperature. Similarly, $P(M_G)$ and $P(L_G)$ denotes the probability of Guwahati having medium and low temperatures respectively. Similarly, we use $P(H_D),\: P(M_D)$ and $P(L_D)$ for Delhi. The following table gives the conditional probabilities for Delhi’s temperature given Guwahati’s temperature.

$$\begin{array}{|c|c|c|c|} \hline & H_D & M_D & L_D \\ \hline H_G & 0.40 & 0.48 & 0.12 \\ \hline M_G & 0.10 & 0.65 & 0.25 \\ \hline L_G & 0.01 & 0.50 & 0.49 \\ \hline \end{array}$$

Consider the first row in the table above. The first entry denotes that if Guwahati has high temperature $(H_G)$ then the probability of Delhi also having a high temperature $(H_D)$ is $0.40;$ i.e., $P(H_D \mid H_G) = 0.40$. Similarly, the next two entries are $P(M_D \mid H_G) = 0.48 \text{ and } P(L_D \mid H_G) = 0.12$. Similarly for the other rows. If it is known that $P(H_G) = 0.2, \: P(M_G) = 0.5$, and $P(L_G)=0.3$, then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is ________.