The distribution of colors of candies in a bag is as follows.

$$\begin{array}{|l| c| c| c| c| c |} \hline \text{Color } & \text{Brown} & \text{Red} & \text{Yellow} & \text{Green} & \text{Orange} \\ \hline \text{Proportion} & 0.3 & 0.2 & 0.2 & 0.2 & 0.1 \\ \hline \end{array}$$

If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?

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Calculate the probability of drawing two of each candy and then add them together.

$$P(\text{same color})= P(B)\cdot P(B) + P(R)\cdot P(R) + P(Y)\cdot P(Y) + P(G)\cdot P(G) + P(O)\cdot P(O)$$ $$= 0.3^2+0.2^2+0.2^2+0.2^2+0.1^2$$ $$= \boxed{0.22}$$