To solve this question we will use the following expression to compute the theoretical probability:
[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]1) We know that there are 4 fives, 4 sixes, and 4 sevens in a standard deck of 52 cards, then, the probability of selecting a 5, 6, or 7 is:
[tex]\frac{4+4+4}{52}\text{.}[/tex]2) Simplifying the above expression we get:
[tex]\frac{12}{52}=\frac{3}{13}\text{.}[/tex]Answer:
[tex]\frac{3}{13}\text{.}[/tex]