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In a game there are 3 jars - I, II, and III. These jars contain identical small gift boxes with either a marble or a star inside them. Jar 1 contains 3 small boxes with stars and 2 with marbles, Jar 2 contains 2 with stars and 3 with marbles, and Jar 3 contains 4 with stars and 1 with marble. The 3 jars are identical, and the probability of selecting any one of them is the same. Bill randomly chooses a jar and then a small box. What is the probability that Bill picks a box with a star in it?