Respuesta :
Answer:
The answer is "0.425".
Step-by-step explanation:
The T be a requirement today that such rains.
The Y be a situation yesterday that now it rained.
The O is a condition for tomorrow to rain.
[tex]P(O| (Y\ AND \ T)) = 0.8\\\\P(O|(Y \ AND \ NOT\ (T)) =0.3\\\\P( O|(NOT \ (Y)\ AND\ T)= 0.4\\\\P( O| NOT\ (Y) \ OR \ NOT \ (T)) =0.2[/tex]
There Arena and morrow overview To Aspects Which will rain:
[tex]Y\ AND \ T, Y \ AND \ NOT \ (T),\ NOT\ (Y) \ AND\ T, \ NOT(Y)\ OR \ NOT(T)[/tex]
Each has the option of [tex]\frac{1}{4}[/tex] INDEPENDENTLY happening.
Its possibility of tomorrow's rain is:
[tex]P(O) = P(O | Y\ AND\ T) P(Y\ AND\ T) + P(O|(Y \ AND \ NOT\ (T))[/tex]
[tex]P((Y\ AND \ NOT\ (T)) + P(O|(\ NOT\ (Y) \ AND \ T))P(\ NOT\ (Y) \ AND\ T) \\\\+ P( O| \ NOT\ (Y)\ OR\ NOT\ (T)) P(\ NOT\ (Y)\ OR\ NOT\ (T))\\\\[/tex]
[tex]=0.8\times \frac{1}{4} +0.3\times \frac{1}{4}+0.4\times \frac{1}{4}+0.2\times \frac{1}{4}\\\\ =\frac{1}{4}(0.8+0.3+0.4+0.2)\\\\= \frac{1.7}{4}\\\\= 0.425[/tex]
