Same colour from two different jars

One jar contains $3$ blue and $4$ red balls; a second jar contains $6$ blue and $4$ red balls. A single ball is drawn at random from each jar, the two draws being independent. Find the chance that both drawn balls share a colour.

$\tfrac{17}{35}$. The draws are independent, so add the two matching cases: both blue has probability $\tfrac37\cdot\tfrac6{10}=\tfrac{18}{70}$ and both red has probability $\tfrac47\cdot\tfrac4{10}=\tfrac{16}{70}$, for a total of $\tfrac{34}{70}=\tfrac{17}{35}$.