Given the set A ={2, 4, 6, 8} and B = {2, 3, 5, 9}.
If a number is picked at random from each of the two sets, what is the probability that their difference is 6 or 7
$\tfrac{1}{256}$
$\tfrac{1}{16}$
$\tfrac{1}{8}$
½
$\begin{align} & \text{Difference that will produce 6 from set A and B are }{{\text{8}}_{\text{from set A}}}\text{ and }{{2}_{\text{from set B}}} \\ & \Pr (selecting\text{ 8)}=\frac{1}{4} \\ & \Pr \text{(selecting 2)}=\frac{1}{4} \\ & \Pr (8and2)=\frac{1}{4}\times \frac{1}{4}=\frac{1}{16} \\ & \text{Difference that will produce 7 from set A and B are }{{\text{9}}_{\text{from set B}}}\text{ and }{{\text{2}}_{\text{from set B}}} \\ & \Pr (selecting\text{ 9)}=\frac{1}{4} \\ & \Pr \text{(selecting 2)}=\frac{1}{4} \\ & \Pr (9and2)=\frac{1}{4}\times \frac{1}{4}=\frac{1}{16} \\ & \Pr (9and2)\text{ or }\Pr (8and2)=\frac{1}{16}+\frac{1}{16}=\frac{1}{8} \\\end{align}$