Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even?

A.
(frac{2}{3}) 
B.
(frac{2}{15}) 
C.
(frac{1}{2}) 
D.
(frac{1}{4})
Correct Answer: Option C
Explanation
(begin{array}{cc} 1 & 2 & 3 & 4\hline 1(1, 1) & (1, 2) & (1, 3) & (1, 4)\ hline 2(2, 1) & (2 , 2) & (2, 3) & (2, 4) \ hline 3(3, 1) & (3, 2) & (3, 3) & (3, 4)\ hline 4(4, 1) & (4, 2) & (4, 3) & (4, 4)end{array})
sample space = 16
sum of nos. removed are (2), 3, (4), 5
3, (4), 5, (6)
(4), 5, (6), 7
(5), 6, 7, (8)
Even nos. = 8 of them
Pr(even sum) = (frac{8}{16})
= (frac{1}{2})