14. Two cards will be selected without replacement from a standard deck of cards. What is the probability that the first is a spade and the second is a club? \( \frac{1}{4} \cdot \frac{1}{4} \)

To find the probability that the first card is a spade and the second card is a club, we first note that there are 13 spades and 13 clubs in a standard deck of 52 cards. When the first card is drawn as a spade, 51 cards remain for the second draw. So, the probability of drawing a spade first is \( \frac{13}{52} \) and the probability of drawing a club second, after a spade has been drawn, is \( \frac{13}{51} \). Therefore, the combined probability is \( \frac{13}{52} \times \frac{13}{51} = \frac{1}{16} \). Remember that the deck gets smaller with each draw. Many people forget to adjust the total number of cards when calculating probabilities in scenarios involving cards being drawn without replacement. It's essential to keep track of how many options are left after each selection to get the correct probability!