Bag A contains $3$ white and $2$ red balls. Bag B contains $6$ white and $3$ red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your answer as a common fraction. [asy] size(140); defaultpen(linewidth(0.7)); pen darkness = linewidth(1.2);
real r = 0.642;
filldraw(circle((-0.931,2.701),r),gray(0.5));

filldraw(circle((1.534,2.633),r),white,darkness);

filldraw(circle((0.356,2.842),r),white,darkness);

filldraw(circle((1.026,2.385),r),gray(0.5));

filldraw(circle((-0.184,2.502),r),white,darkness);

[/asy]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Bag A contains $3$ white and $2$ red balls. Bag B contains $6$ white and $3$ red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your answer as a common fraction. [asy] size(140); defaultpen(linewidth(0.7)); pen darkness = linewidth(1.2);
real r = 0.642;
filldraw(circle((-0.931,2.701),r),gray(0.5));

filldraw(circle((1.534,2.633),r),white,darkness);

filldraw(circle((0.356,2.842),r),white,darkness);

filldraw(circle((1.026,2.385),r),gray(0.5));

filldraw(circle((-0.184,2.502),r),white,darkness);

[/asy]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac 9{20}
Bag A contains $3$ white and $2$ red balls. Bag B contains $6$ white and $3$ red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your answer as a common fraction. [asy] size(140); defaultpen(linewidth(0.7)); pen darkness = linewidth(1.2);
real r = 0.642;
filldraw(circle((-0.931,2.701),r),gray(0.5));

filldraw(circle((1.534,2.633),r),white,darkness);

filldraw(circle((0.356,2.842),r),white,darkness);

filldraw(circle((1.026,2.385),r),gray(0.5));

filldraw(circle((-0.184,2.502),r),white,darkness);

[/asy]
train