1)"P(N\\cap E)=P(E)\\cdot P(N|E)=0.25\\cdot 0.95=\\frac{19}{80}"
2)"P(N)=P(N\\cap (E\\cup S))=P((N\\cap E)\\cup (N\\cap S))" . Since "(N\\cap E)\\cap (N\\cap S)=N\\cap (E\\cap S)=N\\cap\\varnothing=\\varnothing" , we have
"P((N\\cap E)\\cup (N\\cap S))=P(N\\cap E)+P(N\\cap S)="
"P(E)P(N|E)+P(S)P(N|S)="
"=0.25\\cdot 0.95+0.75\\cdot 0.8=\\frac{67}{80}"
3)"P(E|N)=\\frac{P(E\\cap N)}{P(N)}=\\frac{19}{67}"
Answer: 1)"\\frac{19}{80}" 2)"\\frac{67}{80}" 3)"\\frac{19}{67}"
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