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## ← 11-19 Happy Grumpy Question Solution

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Unit 11 19.mp4 Happy Grumpy Answer.mp4

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Showing Revision 1 created 11/28/2012 by Amara Bot.

1. [Thrun] Once again let's calculate the probability of rain on day 1.
2. This one is easy because we know it is raining on day 0,
3. so it's 0.6, the 0.6 over here.
4. This expression over here is expanded by a Bayes rule as applied over here.
5. Probability of happiness during rain is 0.4,
6. the probability of rain was said to be just 0.6,
7. and we divide by 0.4 times 0.6 plus 0.9 times 0.4, which is 1 minus 0.6.
8. And that resolves simply to 0.4 if you work it all out.
9. So the interesting thing here is if you were just to run the Markov chain,
10. on day 1 we have a 0.6 chance of rain,
11. but the fact that I observed myself to be happy reduces the chance of rain to 0.4.