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Let S be the sample space of all 3 x 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given by
E1 = {A ∈ S : det A = 0} and
E2 ={A ∈ S : sum of entries of A is 7}
If a matrix is chosen at random from S, then the conditional probability P(E1/E2) equals _____
    Correct answer is '0.50'. Can you explain this answer?
    Verified Answer
    Let S be the sample space of all 3 x 3 matrices with entries from the ...
    n(E2) = arrangement of 7, 1 and 2 or
    both zero should be in a row or a column
    (number of ways of arranging of (1, 0, 0) = 3 and arrangement of row = 3
    total = 9 in same way for (1, 0, 0) for columns number of ways will be = 9 total ways = 18
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    Most Upvoted Answer
    Let S be the sample space of all 3 x 3 matrices with entries from the ...

    Understanding the Problem:

    Given:
    - Sample space S: Set of all 3x3 matrices with entries from {0, 1}
    - Events:
    - E1 = {A ∈ S : det(A) = 0}
    - E2 = {A ∈ S : sum of entries of A is 7}

    We need to find the conditional probability P(E1/E2).

    Calculating Conditional Probability:

    To find P(E1/E2), we first need to calculate:
    - P(E1 ∩ E2) = Number of matrices in S that satisfy both E1 and E2
    - P(E2) = Number of matrices in S that satisfy E2

    Then, we can use the formula for conditional probability:
    P(E1/E2) = P(E1 ∩ E2) / P(E2)

    Calculating P(E1 ∩ E2):

    To find matrices that satisfy both E1 and E2:
    - For E1: det(A) = 0 means the matrix is singular
    - For E2: sum of entries is 7

    We need to find matrices in S that are singular and have a sum of entries equal to 7.

    Calculating P(E2):

    To find matrices that satisfy E2:
    - The sum of entries in a 3x3 matrix can range from 0 to 9
    - We need to find matrices in S that have a sum of entries equal to 7.

    Final Calculation:

    After calculating P(E1 ∩ E2) and P(E2), we can find:
    P(E1/E2) = P(E1 ∩ E2) / P(E2)

    Therefore, the conditional probability P(E1/E2) equals 0.50.
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    Let S be the sample space of all 3 x 3 matrices with entries from the ...
    Correct answer is'0.50'
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    Let S be the sample space of all 3 x 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given byE1 = {A∈ S : det A = 0} andE2 ={A∈ S : sum of entries of A is 7}If a matrix is chosen at random from S, then the conditional probability P(E1/E2) equals _____Correct answer is '0.50'. Can you explain this answer?
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    Let S be the sample space of all 3 x 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given byE1 = {A∈ S : det A = 0} andE2 ={A∈ S : sum of entries of A is 7}If a matrix is chosen at random from S, then the conditional probability P(E1/E2) equals _____Correct answer is '0.50'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let S be the sample space of all 3 x 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given byE1 = {A∈ S : det A = 0} andE2 ={A∈ S : sum of entries of A is 7}If a matrix is chosen at random from S, then the conditional probability P(E1/E2) equals _____Correct answer is '0.50'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let S be the sample space of all 3 x 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given byE1 = {A∈ S : det A = 0} andE2 ={A∈ S : sum of entries of A is 7}If a matrix is chosen at random from S, then the conditional probability P(E1/E2) equals _____Correct answer is '0.50'. Can you explain this answer?.
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