$\begin{array}{|c|c|c|c|} \hline & X = a & X = b & Total \\ \hline Y = c & 20 & 70 & 90 \\ \hline Y = d & 15 & 45 & 60 \\ \hline Total & 35 & 115 & 150 \\ \hline \end{array}$
$P(X = b, Y \ne c)$
$P(X = b) \rightarrow \frac{115}{150}$
$P(Y \ne c) \rightarrow 1 - P(Y \ne c) \rightarrow 1 - \frac{90}{150} \rightarrow \frac{60}{150}$
$P(X = b\hspace{.5em} \cap \hspace{.5em} Y \ne c) \rightarrow P(X = b) + P(Y \ne c) - P(X = b\hspace{.5 em} \cup\hspace{.5 em} Y \ne c) \rightarrow \frac{?}{?}$
im not sure how to calculate the prob since im getting 0 if i do this rn and off using the formula, using the table i can see its $\frac{45}{150}$.
