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Conditional Probabilities, Seattle Rain, And Tricky Friends

Discovered on 31 May 09:00 AM CDT.

- The first time I saw this problem, I thought “only if all 3 of my friends lied to me then it would mean it’s not raining in Seattle”.
- In a state of the world where it is raining, our friends can’t have answered “yes” and lied (to lie, they would have had to have replied “no”).
- That’s not possible either — all of them said “yes” and to lie in the state of the world where it’s raining requires a “no”.
- Because in the sunny state of the world, our friends would have had to respond “no, it’s not raining” in order to be telling the truth.
- No, actually we’re estimating the probability of rain given that our friends all said “yes, it’s raining”.
- Let’s think back to our problem — we want to know the probability that it is raining when all 3 of our friends say “yes, it’s raining”.

Read full article on
towardsdatascience.com.

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Conditional Probabilities, Seattle Rain, And Tricky Friends

Discovered on 31 May 12:00 AM CDT.

- The first time I saw this problem, I thought “only if all 3 of my friends lied to me then it would mean it’s not raining in Seattle”.
- In a state of the world where it is raining, our friends can’t have answered “yes” and lied (to lie, they would have had to have replied “no”).
- That’s not possible either — all of them said “yes” and to lie in the state of the world where it’s raining requires a “no”.
- Because in the sunny state of the world, our friends would have had to respond “no, it’s not raining” in order to be telling the truth.
- No, actually we’re estimating the probability of rain given that our friends all said “yes, it’s raining”.
- Let’s think back to our problem — we want to know the probability that it is raining when all 3 of our friends say “yes, it’s raining”.

Read full article on
towardsdatascience.com.