When a weather is randomly determined, there is a 75% chance that forecast will show that weather. If not, a separate "forecast" weather will be determined randomly again, using the same rules as for the "true" weather. It can actually show the same weather, even if the forecast was not accurate, which is common especially in the months when one weather type is dominant. Therefore the chance for the weather forecast to lie is pretty small.
example: 95% chance for clear, 5% chance for mud
weather clear, forecast accurate: 0.95*0.75 = 0.7125
weather clear, forecast not accurate, forecast clear: 0.95*0.25*0.95 = 0.225625
weather clear, forecast not accurate, forecast mud: 0.95*0.25*0.05 = 0.011875
weather mud, forecast accurate: 0.05*0.75 = 0.0375
weather mud, forecast not accurate, forecast clear: 0.05*0.25*0.95 = 0.011875
weather mud, forecast not accurate, forecast mud: 0.05*0.25*0.05 = 0.000625
check to see if all combinations are covered:
0.7125 + 0.225625 + 0.011875 + 0.0375 + 0.011875 + 0.000625 = 1, which is correct
Chance of clear forecast turning to mud is the fifth option with 1.1875% chance.
Only option 3 and 5 are where forecast weather is different from true weather, which means forecast has actually 97,625% chance to be "accurate" (defined as forecast weather the same as true weather) in this case. It will be less reliable in periods like May - early June.