At Rachelle's school an $A$ counts 4 points, a $B$ 3 points, a $C$ 2 points, and a $D$ 1 point. Her GPA on the four classes she is taking is computed as the total sum of points divided by 4. She is certain that she will get $A$s in both Mathematics and Science, and at least a $C$ in each of English and History. She thinks she has a $\tfrac{1}{6}$ chance of getting an $A$ in English, and a $\tfrac{1}{4}$ chance of getting a $B$. In History, she has a $\tfrac{1}{4}$ chance of getting an $A$, and a $\tfrac{1}{3}$ chance of getting a $B$, independently of what she gets in English. What is the probability that Rachelle will get a GPA of at least 3.5?