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

Question

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 (A) 90 % (B) 84 % (C) 80 % (D) 96 %

Tardigrade Admin · Accepted Answer

S = 2,3,5,7,11 Total ways in which A and B can be chosen =( 5 C 4 ⋅ 4 !)2=(5 !)2 P ( E )=1- P ( A and B does not contain the element 2) 1-((4 !)2/(5 !)2)=1-(1/25)=(24/25)=96 %

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 $A B$ has atleast one odd entry, is

$90%$

$84%$

$80%$

$96%$

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

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 ∈S. The chance that the matrix AB has atleast one odd entry, is

90%

84%

80%

96%