15. Josic takes a card at random from this pack and koops it Then she takes a second card at random. Find the probability that she takes one odd number and one even number (in either order).

To find the probability that Josic picks one odd number and one even number from a standard deck of cards, we can break it down. There are 26 even cards (2, 4, 6, 8, 10, and all face cards) and 26 odd cards (1, 3, 5, 7, 9, and all face cards). The total number of ways to choose 2 cards from 52 is calculated as \( \binom{52}{2} = 1326 \). There are two successful scenarios where she could pick one odd and one even card: first an odd card, then an even card, or vice versa. - **Odd first, then even:** The number of odd cards is 26 and after picking one odd card, 26 even cards remain, so the count for this combination is \( 26 \times 26 = 676 \). - **Even first, then odd:** Similarly, it would also yield another \( 26 \times 26 = 676 \). Adding these gives us \( 676 + 676 = 1352 \) successful outcomes. Thus, the probability is given by the ratio of successful outcomes to the total outcomes, \( \frac{1352}{1326} \). Simplifying that fraction gives you the neat probability. Finally, after reducing, we find that \( \frac{676}{663} \) is the sought probability. But don't lose track; just remember to multiply and simplify!