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 As in both Mathematics and Science, and at least a \mathrm{C} in each of English and History. She thinks she has a \dfrac{1}{6} chance of getting an A in English, and a \dfrac{1}{4} chance of getting a B. In History, she has a \dfrac{1}{4} chance of getting an A, and a \dfrac{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 ?
Answer Choices
A. \dfrac{11}{72}
B. \dfrac{1}{6}
C. \dfrac{3}{16}
D. \dfrac{11}{24}
E. \dfrac{1}{2}