Question 15
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 C in each of English and History. She thinks she has a $\dfrac16$ chance of getting an A in English, and a $\dfrac14$ chance of getting a B. In History, she has a $\dfrac14$ chance of getting an A, and a $\dfrac13$ 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 $3.5?$