Question 1073869
Take the time to write your questions more coherently.
There'll be a higher probability it gets answered.
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So look at the possible outcomes. 
You choose a red ball from the first bag, then choose a green ball from the second. 
Or you choose a green ball from the first bag, then choose a red ball from the second. 
The first case P(RG),
{{{P(R[1])=4/7}}}
{{{P(G[2])=1/3}}}
So,
{{{P(RG)=(4/7)(1/3)=4/21}}}
The second case P(GR),
{{{P(G[1])=3/7}}}
{{{P(R[2])=2/3}}}
So,
{{{P(GR)=(3/7)(2/3)=6/21}}}
So then together,
{{{P=P(RG)+P(GR)}}}
{{{P=4/21+6/21}}}
{{{P=10/21}}}