In a standard 52-card deck, there are 4 suits: hearts, diamonds, clubs, and spades. Each suit contains one 10 and one Jack.
- Number of 10s in the deck: 4 (one from each suit)
- Number of Jacks in the deck: 4 (one from each suit)
To find the total number of favorable outcomes (selecting a 10 or a Jack), you add the number of 10s and Jacks together:
\[ \text{Total favorable outcomes} = 4 , (\text{10s}) + 4 , (\text{Jacks}) = 8 \]
The total number of possible outcomes (the total number of cards in the deck) is 52.
Now, the probability \( P \) of selecting a 10 or a Jack can be calculated using the formula:
\[ P(\text{10 or Jack}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{8}{52} \]
To simplify this fraction:
\[ P(\text{10 or Jack}) = \frac{8}{52} = \frac{2}{13} \]
Thus, the probability of selecting a 10 or a Jack is:
\[ \boxed{\frac{2}{13}} \]
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