A bag contains 10 balls numbered from 1 to 10.
Given that the sum of the numbers on two balls randomly drawn from the bag is 15, what is the probability that ball number 7 was drawn?
A) $\frac { 2 } { 3 }$
B) $\frac { 2 } { 5 }$
C) $\frac { 2 } { 7 }$
D) $\frac { 1 } { 2 }$
E) $\frac { 1 } { 3 }$

Two different digits are randomly selected from the set $A = \{ 1,2,3,4,5,6,7 \}$.
Given that the product of the selected digits is an even number, what is the probability that the sum of these digits is also an even number?
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 5 }$
E) $\frac { 1 } { 6 }$