2. When lightning seen, rain forcasted at 90%

Raja

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Hello, Here are some questions and my attempts, can someone kindly guide me.

Problem 2. Bayes Theorem: Weather and Climate

Based on her prior experience, when she sees lightning, a weather forecaster gives a forecast of 90% chance of rain. On the other hand, if she just sees the thunderclouds in the charts, she gives a 60% chance of rain. Overall, there are equal chances of thunderclouds or lightning occurring. She thus uses her expert judgment of past events, along with the particular charts of that day, to make a forecast. Given that it is raining, calculate the probability that lightning was seen before the storm. (Hints: Construct a contingency table of probabilities of different events and combinations [for example, thunder and rain]. Assume that it rains half the time, and is dry half the time.)


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