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 determine the probability that Josic draws one odd-numbered card and one even-numbered card from a standard 52-card deck (assuming "this pack" refers to a standard deck), we can follow these steps: ### Step 1: Identify the Number of Odd and Even Cards - **Odd-numbered cards**: Ace (1), 3, 5, 7, 9, Jack (11), King (13) - **Total per suit**: 7 - **Total in deck**: 7 × 4 = 28 - **Even-numbered cards**: 2, 4, 6, 8, 10, Queen (12) - **Total per suit**: 6 - **Total in deck**: 6 × 4 = 24 ### Step 2: Calculate the Probability for Both Orders There are two possible orders for drawing one odd and one even card: 1. **First card odd, second card even:** \[ P(\text{Odd first, Even second}) = \frac{28}{52} \times \frac{24}{51} \] 2. **First card even, second card odd:** \[ P(\text{Even first, Odd second}) = \frac{24}{52} \times \frac{28}{51} \] Since these two scenarios are mutually exclusive, we add their probabilities: \[ P(\text{One Odd and One Even}) = \frac{28}{52} \times \frac{24}{51} + \frac{24}{52} \times \frac{28}{51} = 2 \times \frac{28 \times 24}{52 \times 51} \] ### Step 3: Simplify the Calculation \[ 2 \times \frac{28 \times 24}{52 \times 51} = 2 \times \frac{672}{2652} = \frac{1344}{2652} = \frac{112}{221} \quad \text{(after simplifying)} \] ### Final Answer The probability that Josic draws one odd-numbered card and one even-numbered card in either order is: \[ \boxed{\dfrac{112}{221}} \]