Pat picked a card from a standard deck, looked at it, and then put it back. he then picked a second card. what is the probability that pat picked a diamond or a jack on either pick? 16/521/5213/5217/52

Picking a random card from a deck, you have a 16/52 probability of picking a Jack or a diamond. That is the probability of getting a jack plus diamond, minus the jack of diamonds so that you don't count that one twice.  
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16/52 because there are 52 cards in a standard deck and there are 13 diamonds and 4 four jacks but you take one away as the jack of diamonds has already been counted and cannot be counted twice. 13+3=16 and do there is a 16/52 probability

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