What is the probability of drawing a diamond from a standard deck of cards on a second draw, given that a diamond was drawn on the first draw and not replaced? twelve over fifty one one over fifty two one over fifty one thirteen over fifty two,

Since you have removed one diamond out of thirteen and not replaced it, the answer is twelve over 51. There are four suits of thirteen cards, so when the first card was drawn, the odds were 13/52 or 1/4 simplified. However, previous events are not a predictor of the future, and so the odds are 12/51.