You have 4 jars. In the largest jar you have three balls numbered 1 to 3. Then you have 3 colored jars. Jar 1 has a red ball and two orange balls. Jar 2 has one orange ball and 2 red balls. Jar 3 has a red ball, an orange ball and a yellow ball. There are two random variables X and Y w/ X being the draw of a single numbered ball from the large jars and Y being a single ball from one of the colored jars, 1 to 3. Respecify the contents of the numbered jars to make them statistically independent. You can increase the number of balls and each jar must contain a different number of red, orange and yellow balls.
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This solution demonstrates conditional and marginal probabilities with balls selected from urns.