You are dealt one card from a 62-card deck. Find the probability that you are dealf a club or a picture card. The probabilly is \( \square \). (Type an integer or a simplified fraction.)

To find the probability of being dealt a club or a picture card from a 62-card deck, we need to follow these steps: 1. **Identify the total number of cards in the deck**: - The total number of cards is \( 62 \). 2. **Identify the number of clubs in the deck**: - In a standard deck, there are 13 clubs. 3. **Identify the number of picture cards in the deck**: - Picture cards are typically the Jack, Queen, and King. In a standard deck, there are 3 picture cards per suit, and since there are 4 suits, the total number of picture cards is \( 3 \times 4 = 12 \). 4. **Calculate the total number of favorable outcomes**: - We need to find the total number of cards that are either clubs or picture cards. However, we must be careful not to double-count the picture cards that are also clubs. - The number of clubs is \( 13 \). - The number of picture cards is \( 12 \). - The number of picture cards that are clubs (Jack of Clubs, Queen of Clubs, King of Clubs) is \( 3 \). Therefore, the total number of favorable outcomes is: \[ \text{Total favorable outcomes} = \text{Number of clubs} + \text{Number of picture cards} - \text{Number of picture cards that are clubs} \] \[ = 13 + 12 - 3 = 22 \] 5. **Calculate the probability**: - The probability \( P \) of being dealt a club or a picture card is given by the ratio of the number of favorable outcomes to the total number of outcomes: \[ P = \frac{\text{Total favorable outcomes}}{\text{Total number of cards}} = \frac{22}{62} \] 6. **Simplify the fraction**: - We can simplify \( \frac{22}{62} \) by dividing both the numerator and the denominator by their greatest common divisor, which is \( 2 \): \[ P = \frac{22 \div 2}{62 \div 2} = \frac{11}{31} \] Thus, the probability that you are dealt a club or a picture card is \( \frac{11}{31} \).