We will use complementary counting to find the probability that the product is not divisible by 4 . Then, we can find the probability that we want by subtracting this from 1 . We split this into 2 cases. Case 1: The product is not divisible by 2. We need every number to be odd, and since the chance we roll an odd number is $\frac{1}{2}$, our probability is $\left(\frac{1}{2}\right)^{6}=\frac{1}{64}$ Case 2: The product is divisible by 2 , but not by 4 . We need 5 numbers to be odd, and one to be divisible by 2 , but not by 4 . There is a $\frac{1}{2}$ chance that an odd number is rolled, a $\frac{1}{3}$ chance that we roll a number satisfying the second condition (only 2 and 6 work), and 6 ways to choose the order in which the even number appears. Our probability is $\left(\frac{1}{2}\right)^{5}\left(\frac{1}{3}\right) \cdot 6=\frac{1}{16}$. Therefore, the probability the product is not divisible by 4 is $\frac{1}{64}+\frac{1}{16}=\frac{5}{64}$. Our answer is $1-\frac{5}{64}=$ (C) $\frac{59}{64}$. 
Una rolls 6 standard 6 -sided dice simultaneously and calculates the product of the 6 numbers obtained. What is the probability that the product is divisible by 4 ? 

A) $\frac{3}{4}$ 
B) $\frac{57}{64}$ 
C) $\frac{59}{64}$ 
D) $\frac{187}{192}$ 
E) $\frac{63}{64}$ 