Saying that the ultimate outcome had a 1 in 4 chance is not wrong, slightly wrong, or less wrong. If the weatherman says there's a 1 in 4 chance of rain, and it rains, he wasn't wrong.
To take it a step further, if that was the forecast 4 days in a row, you would expect it to rain one of those days.
Not necessarily.
There is a 0.750.750.75*0.75 or a 31% chance of no rain at all
I'm not saying it's certain, but it's what I'd expect. It raining on one day out of 4 is the most common case.
No, but it means that the weatherman isn't particularly effective at forecasting the weather.
Only if they say that every day, and it rains every day. If the most likely outcome happened every time, then the model is likely wrong/under-confident. The prediction is never going to be 100% accurate until the event is happening/has happened. Up until then, there's always a chance you're wrong or something can change. Being wrong once isn't necessarily a sign that the whole system is messed up.
No it doesn’t, and this is a fundamental misunderstanding of how probabilistic forecasting works. If it rains 9 out of 10 times a weatherman says there is a 30% chance of rain, they are a bad weatherman, but they aren’t much worse than if it rained 0 out of 10 times they predicted a 30% chance of rain. A weatherman accurately assessing the probability of the weather forecast would see it rain around 3 out of 10 days they say there is a 30% chance of rain.