Bonjour,
[tex]P(F) = \frac{60}{400} = \frac{3}{20} \\ \\
P(E) = \frac {140}{400} = \frac{7}{20}\\ \\
P(F\cap E) = \frac{45}{400} = \frac{9}{80}\\ \\
P(F\cap E^C) = P(F) - P(F\cap E) = \frac{3}{20} - \frac{9}{80} = \frac{3}{80}\\ \\
P(E\cap F^C) = P(E) - P(E\cap F) = \frac{7}{20} - \frac{9}{80} = \frac{19}{80}\\ \\
P(F^C \cap E^C) = 1 - P(F\cup E) = 1 - (P(F)+P(E)-P(F\cap E))\\ \\
P(F^C \cap E^C) = 1 - \frac{3}{20} - \frac{7}{20} + \frac{9}{80} = \frac{49}{80}\\ \\
[/tex]
[tex]P(F\cup E) = P(F) + P(E) - P(F\cap E) = \frac{3}{20} + \frac{7}{20} - \frac{9}{80} = \frac{31}{80}[/tex]
