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?

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?

Answer Details

$\begin{array}{cccc}1& 2& 3& 4\\ 1(1,1)& (1,2)& (1,3)& (1,4)\\ 2(2,1)& (2,2)& (2,3)& (2,4)\\ 3(3,1)& (3,2)& (3,3)& (3,4)\\ 4(4,1)& (4,2)& (4,3)& (4,4)\end{array}$
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) = $\frac{8}{16}$
= $\frac{1}{2}$