Let \( \mathrm{S} \) be the sample space of all \( 3 \times 3 \) matrices with entries from the ... VIDEO
Let \( \mathrm{S} \) be the sample space of all \( 3 \times 3 \) matrices with entries from the set \( \{0,1\} \). Let the events \( \mathrm{E}_{1} \) and \( \mathrm{E}_{2} \) be given by
\( P \)
\[
\begin{array}{l}
\mathrm{E}_{1}=\{\mathrm{A} \in \mathrm{S}: \operatorname{det} \mathrm{A}=0\} \text { and } \\
\mathrm{E}_{2}=\{\mathrm{A} \in \mathrm{S}: \text { sum of entries of } \mathrm{A} \text { is } 7\} .
\end{array}
\]
W
If a matrix is chosen at random from \( \mathrm{S} \), then the conditional probability \( \mathrm{P}\left(\mathrm{E}_{1} \mid \mathrm{E}_{2}\right) \) equals
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