Solution:
Given:
From the deck of cards given,
[tex]\begin{gathered} number\text{ of 7}=4 \\ number\text{ of diamonds}=13 \\ number\text{ of 7 and diamond}=1 \\ Total\text{ number of cards}=52 \end{gathered}[/tex]Hence, the probability of picking a 7 or a diamond would be;
[tex]\begin{gathered} P(7\text{ or diamond\rparen}=P(7)+P(diamond)-P(7\text{ and diamond\rparen} \\ P(7\text{ or diamond\rparen}=\frac{4}{52}+\frac{13}{52}-\frac{1}{52} \\ P(7\text{ or diamond\rparen}=\frac{4+13-1}{52} \\ P(7\text{ or diamond\rparen}=\frac{16}{52} \\ P(7\text{ or diamond\rparen}=\frac{4}{13} \end{gathered}[/tex]Therefore, the probability of pickng a 7 or a diamond is;
[tex]\frac{4}{13}[/tex]