Gate2018 cs Q47
The following table gives the conditional probabilities for Delhi’s temperature given Guwahati’s temperature.
| HD | MD | LD | |
| HG | 0.40 | 0.48 | 0.12 |
| MG | 0.10 | 0.65 | 0.25 |
| LG | 0.01 | 0.50 | 0.49 |
Consider the first row in the table above. The first entry denotes that if Guwahati has high temperature (HG) then the probability of Delhi also having a high temperature (HD) is 0.40; i.e., P(HD ∣ HG) = 0.40. Similarly, the next two entries are P(MD ∣ HG) = 0.48 and P(LD ∣ HG) = 0.12. Similarly for the other rows.
If it is known that P(HG) = 0.2, P(MG) = 0.5, and P(LG) = 0.3, then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _______ .
Note – Numerical Type question.
- Option : A
- Explanation : The condition probability table given is
P(HG) = 0.2 P(MG) = 0.5 P(LG) = 0.3 Drawing the tree diagram for HD we get,HD MD LD HG 0.40 0.48 0.12 MG 0.10 0.65 0.25 LG 0.01 0.50 0.49 
From diagram, P(HG ∩ HD) = 0.2x0.4
P(HD) = 0.2x0.4+0.5x0.1+0.3x0.01 = 0.133
Required probability,
P(HG | HD) = (0.2x0.4)/0.133 = 0.60
