Probability (all possibilities) can be >1 ?

[Merlin3189]

Reading a book "Simply AI" (from DK !) came across this diagram.

I know I'm old and out of practice, but these probabilities don't make sense to me.
The text implies that these are states in a Markov chain, but the probabilities mean the three states cannot be mutually exclusive. So (to me) this cannot show a complete set of Markov states, which would have to include states like "rain and cloud", "sun and cloud", "sun rain and cloud". Then this diagram would be confusing, because the three states shown cannot be "sun only", "rain only", "cloudy only".
Anyhow, I'd be interested if anyone can explain this diagram. I suspect that being a DK publication, it's not intended to be taken too seriously, so maybe there is no explanation.

 

[FactChecker]

The labels of the three states are abbreviations. IMO, they are meant to be disjoint states. "Cloudy" means "Enough clouds to not be called sunny, and not enough rain to be called rainy".
I wouldn't be too critical of the book. It's a natural abbreviation to make.
If the main subject were the weather I would expect a more precise definition of the terms somewhere.

 

[Dale]

It is wrong.

 

[FactChecker]

I didn't notice that some of the outflow probabilities do not add up to 100% when the circular "stay in same state" are included. Flows out of Rainy add up to 150% (including the circular "stay in Rainy" flow), flows out of Sunny add up to 110% and flows out of Cloudy add up to 40%. It's all wrong.

 

[Dale]

It wouldn't be a Markov chain, but since no transition probability is greater than 100%, you could consider each to be an independent probability. So one state could transition to multiple states or even to no state. This latter possibility would eventually terminate the chain with no state.

 

[DaveC426913]

Anyhow, I'd be interested if anyone can explain this diagram.

Didn't you answer your own question?

"...Simply AI..."

Since when is AI accurate about anything?

I suspect that being a DK publication

What is DK? Oh, you mean it's a children's book publication.

 

[Mark44]

What is DK?

I suspect that "from DK" means that it is from Denmark.

 

[pbuk]

I suspect that "from DK" means that it is from Denmark.

https://en.wikipedia.org/wiki/Dorling_Kindersley