1. Tardigrade
  2. Question
  3. Mathematics
  4. Let S be a set consisting of first five prime numbers. Suppose A and B are two matrices of order 2 each with distinct entries ∈ S. The chance that the matrix AB has atleast one odd entry, is

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Q. Let $S$ be a set consisting of first five prime numbers. Suppose $A$ and $B$ are two matrices of order 2 each with distinct entries $\in S$. The chance that the matrix $AB$ has atleast one odd entry, is

Probability - Part 2

Solution:

$S =\{2,3,5,7,11\}$
Total ways in which $A$ and $B$ can be chosen $=\left({ }^5 C _4 \cdot 4 !\right)^2=(5 !)^2$ $P ( E )=1- P ( A$ and $B$ does not contain the element 2$)$
$1-\frac{(4 !)^2}{(5 !)^2}=1-\frac{1}{25}=\frac{24}{25}=96 \% $