You have one suit of a standard deck of playing cards and you use their denominations as the vertex names in a roo tree. The Ace is the designated vertex, the root of the tree. The Jack, Queen, and King are children of the Ace. The prime number cards are children of the King; the even number cards that are not prime are children of the Que and the odd number cards that are not prime are children of the Jack. For all three questions answer with a fraction, for example, 1/2 is a fraction. If you randomly pick a leaf from the tree, what is the probability that you picked a child of the Jack or the King? If you randomly pick a vertex from the tree, what is the probability that it is a parent? What is the probability of randomly picking the King given that you have picked a parent from the tree?

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