The probability of A or B when you have mutually exclusive events (ones that can't happen at the same time) is:
[tex]P(\text{A or B)=P(A)+P(B)}[/tex]Let's call A the probability of getting a 4, B the probability of getting a 5 and C the probability of getting a 6.
Then in the deck, there are 4 cards with the number 4, then the probability of A is:
[tex]P(A)=\frac{4}{52}[/tex]There are 4 cards with the number 5, and 4 cards with the number 6, then the probabilities of B and C are:
[tex]\begin{gathered} P(B)=\frac{4}{52} \\ P(C)=\frac{4}{52} \end{gathered}[/tex]Thus, the probability of A or B or C is:
[tex]\begin{gathered} P(A\text{ or B or C)=P(A)+P(B)+P(C)} \\ P(A\text{ or B or C)=}\frac{4}{52}+\frac{4}{52}+\frac{4}{52} \\ P(A\text{ or B or C)=}\frac{4+4+4}{52} \\ P(A\text{ or B or C)=}\frac{12}{52} \\ \text{ Simplify} \\ P(A\text{ or B or C)=}\frac{3}{13} \end{gathered}[/tex]Answer: The probability of that card being a 4, 5 or 6 is 3/13
