OE


First, we will calculate the total number of ways of selecting two tiles randomly out of 6.
This can be done in $𝐶^6_2$ ways.
Now, for the sum of numbers to be a multiple of 2, it implies that the sum must be
EVEN.
That means for the sum to be even there are two possibilities:
(i) Either both must be EVEN numbers
(ii) Both must be ODD numbers.
There are 3 EVEN numbered tiles (2, 4, 6) and 3 ODD numbered tiles (1, 3, 5).
Thus, total number of ways of selecting two EVEN number tiles = $C^3_2$
Total number of ways of selecting two ODD number tiles =$C^3_2$

Therefore,
Total number of ways of selecting 2 even or 2 odd tiles =$C^3_2+C^3_2$


Probability will be

$\dfrac{C^3_2+C^3_2}{C^6_2}=\dfrac{3+3}{\frac{6 \times 5}{2}}=\frac{6}{15}=\frac{2}{5}$