Let \( \mathrm{S} \) be the sample space of all \( 3 \times 3 \) matrices with entries from the ...

Channel:
Subscribers:
449,000
Published on ● Video Link: https://www.youtube.com/watch?v=Mpll5saGY50



Duration: 10:55
4 views
0


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
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2022-12-01Box 1 contains three cards bearing numbers, \( 1,2,3 \); box 2 contains five cards bearing numbe...
2022-12-01Is the force between two point electric charges \( q_{1} \) and \( q_{2} \) kept at some distanc...
2022-12-01A block of mass \( 0.18 \mathrm{~kg} \) is attached to a spring of force-constant \( 2 \mathrm{~...
2022-12-01Box 1 contains three cards bearing numbers, \( 1,2,3 \); box 2 contains five cards bearing numbe...
2022-12-01If \( |\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}|=|\overrightarrow{\mathrm{...
2022-12-01A vector \( \vec{A} \) points vertically upward and \( \vec{B} \) points towards north. The vect...
2022-12-01Two vectors \( \vec{A} \) and \( \vec{B} \) are such that \( \vec{A}+\vec{B}=\vec{A}-\vec{B} \)....
2022-12-01A box \( B_{1} \) contains 1 white ball, 3 red balls and 2 black balls. Another box \( B_{2} \) ...
2022-12-01The angle between vectors \( (\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}) \)...
2022-12-01Area of a parallelogram, whose diagonals are \( 3 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\math...
2022-12-01Let \( \mathrm{S} \) be the sample space of all \( 3 \times 3 \) matrices with entries from the ...
2022-12-01For a body, angular velocity \( \vec{\omega}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{...
2022-12-01If the vectors \( (\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}) \) and \( 3 \hat{\mathrm{...
2022-12-01If \( \overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}=\overrightarrow{0} \) and \...
2022-12-01Let \( \mathrm{E} \) and \( \mathrm{F} \) be two independent events. The probability that exactl...
2022-12-01The minimum number of times a fair coin needs to be tossed, so that the probability of getting P...
2022-12-01Of the three independent events \( \mathrm{E}_{1}, \mathrm{E}_{2} \) and \( \mathrm{E}_{3} \), t...
2022-12-01Football teams \( \mathrm{T}_{1} \) and \( \mathrm{T}_{2} \) have to play two games against each...
2022-12-01Football teams \( \mathrm{T}_{1} \) and \( \mathrm{T}_{2} \) have to play two games against each...
2022-12-01A signal which can be green or red with probability \( \frac{4}{5} \) and \( \frac{1}{5} \) resp...
2022-12-01Three boys and two girls stand in a queue. The probability, that the number of boys ahead of eve...