$\text{A}$ and $\text{B}$ are friends. They decide to meet between $\text{1 PM}$ and $\text{2 PM}$ on a given day. There is a condition that whoever arrives first will not wait for the other for more than $15$ minutes. The probability that they will meet on that day is
- $\frac{1}{4}$
- $\frac{1}{16}$
- $\frac{7}{16}$
- $\frac{9}{16}$