GATE CS 2018 Set 1 — Question 54
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Engineering Mathematics → Probability & Statistics → Bayes' Theorem
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Question
Consider Guwahati (G) and Delhi (D) whose temperatures can be classified as high (), medium () and low (). Let denote the probability that Guwahati has high temperature. Similarly, and denotes the probability of Guwahati having medium and low temperatures respectively. Similarly, we use , and for Delhi.The following table gives the conditional probabilities for Delhi’s temperature given Guwahati’s temperature.
Consider the first row in the table above. The first entry denotes that if Guwahati has high temperature () then the probability of Delhi also having a high temperature () is 0.40; i.e., . Similarly, the next two entries are and . Similarly for the other rows.If it is known that , , and , then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _______.
| 0.40 | 0.48 | 0.12 | |
| 0.10 | 0.65 | 0.25 | |
| 0.01 | 0.50 | 0.49 |
Correct answer
0.6 to 0.62
Solution
We need to find the conditional probability that Guwahati has a high temperature given that Delhi has a high temperature, denoted as .According to Bayes' Theorem:First, we calculate the total probability of Delhi having a high temperature, , using the Law of Total Probability:From the given table and problem statement:
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