JEE MainMathematicsToughProbability

Let A = set of all 3 × 3 matrices having entries +1 or -1, if a
matrix B from the set A is chosen randomly, then the probability that
the product of the elements of any row or any column of B is -1 is

Show answer and solution

Total = 2^9

\ Let\ B = \left| a_{1}\ \ \ \ a_{2}\ \ \ \ a_{3}\ b_{1}\ \ \ \ b_{2}\ \ \ \ b_{3}\ c_{1}\ \ \ \ c_{2}\ \ \ \ c_{3}\ \right|

The first row has 4 combination

\{ 1,\ 1, - 1\},\{ - 1,\ 1,\ 1\},\{ 1, - 1,\ 1\},\{ - 1, - 1, - 1\}

.
Now for each combination the rest entries can be filled in 4 ways
Hence, Probability is

\frac{16}{2^{9}} = \frac{1}{32}

Source: Grass-G / M-08 Mathematics Paper 23 October.docx

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