Exercício: soma mais provável.

Os números naturais de $1$ a $10$ foram escritos, um a um, sem repetição, em dez bolas de pingue-pongue. Se duas delas forem escolhidas ao acaso, qual o valor mais provável da soma dos números sorteados?

$2$: $(1, 1)$

$3$: $(1, 2)$, $(2, 1)$

$4$: $(1, 3)$, $(2, 2)$, $(3, 1)$

$5$: $(1, 4)$, $(2, 3)$, $(3, 2)$, $(4, 1)$

$6$: $(1, 5)$, $(2, 4)$, $(3, 3)$, $(4, 2)$, $(5, 1)$

$7$: $(1, 6)$, $(2, 5)$, $(3, 4)$, $(4, 3)$, $(5, 2)$, $(6, 1)$

$8$: $(1, 7)$, $(2, 6)$, $(3, 5)$, $(4, 4)$, $(5, 3)$, $(6, 2)$, $(7, 1)$

$9$: $(1, 8)$, $(2, 7)$, $(3, 6)$, $(4, 5)$, $(5, 4)$, $(6, 3)$, $(7, 2)$, $(8, 1)$

$10$: $(1, 9)$, $(2, 8)$, $(3, 7)$, $(4, 6)$, $(5, 5)$, $(6, 4)$, $(7, 3)$, $(8, 2)$, $(9, 1)$

$11$: $(1, 10)$, $(2, 9)$, $(3, 8)$, $(4, 7)$, $(5, 6)$, $(6, 5)$, $(7, 4)$, $(8, 3)$, $(9, 2)$, $(10, 1)$

$12$: $(2, 10)$, $(3, 9)$, $(4, 8)$, $(5, 7)$, $(6, 6)$, $(7, 5)$, $(8, 4)$, $(9, 3)$, $(10, 2)$

$13$: $(3, 10)$, $(4, 9)$, $(5, 8)$, $(6, 7)$, $(7, 6)$, $(8, 5)$, $(9, 4)$, $(10, 3)$

$14$: $(4, 10)$, $(5, 9)$, $(6, 8)$, $(7, 7)$, $(8, 6)$, $(9, 5)$, $(10, 4)$

$15$: $(5, 10)$, $(6, 9)$, $(7, 8)$, $(8, 7)$, $(9, 6)$, $(10, 5)$

$16$: $(6, 10)$, $(7, 9)$, $(8, 8)$, $(9, 7)$, $(10, 63)$

$17$: $(7, 10)$, $(8, 9)$, $(9, 8)$, $(10, 7)$

$18$: $(8, 10)$, $(9, 9)$, $(10, 8)$

$19$: $(9, 10)$, $(10, 9)$

$20$: $(10, 10)$

Logo a soma mais provável é $11$.