Solutions - 5020-06

(a)

Use $P[M]=P[M\cap C]+P[M\cap C^c]$ to isolate $P[M\cap C^c]$:

$$\begin{array}{c}P[M\cap C^c]=P[M]-P[M\cap C]\\ \\ \gg \gg 0.375-0.15\gg \gg 0.225\end{array}$$

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(b)

Apply De Morgan’s law and inclusion-exclusion:

$$\begin{array}{c}P[M^c\cap C^c]=1-P[M\cup C]\\ \\ \gg \gg 1-(0.375+0.45-0.15)\gg \gg 0.325\end{array}$$