Verified answer

[tex]\large\text{$Letra ~d) ~\dfrac{12}{25} $}[/tex]

                                            [tex]\Large\text{$ Probabilidade $}[/tex]

Encontrar o número de casos possíveis de se colocar as duas peças no tabuleiro

São 25 casas e duas estarão ocupadas = 23 casas restantes

[tex]C_{25}^2 = \dfrac{25!}{23! ~. ~2!} \\\\\\C_{25}^2 = \dfrac{25 ~. ~24 ~. ~23!}{23! ~. ~2!} \\\\\\C_{25}^2 = \dfrac{25 ~. ~24 ~. ~\not 23!}{\not 23! ~. ~2!} \\\\\\C_{25}^2 = \dfrac{25 ~. ~24}{2} \\\\\\C_{25}^2 = \dfrac{600}{2} \\\\\\C_{25}^2 = 300 ~ casos ~poss\acute{i}veis[/tex]

Casos favoráveis para a peça branca, contar as casas brancas.

[tex]C_{12}^2 = \dfrac{12!}{10! ~. ~2!} \\\\\\C_{12}^2 = \dfrac{12 ~. ~11 ~. 10!}{10! ~. ~2!} \\\\\\C_{12}^2 = \dfrac{12 ~. ~11 ~. \not 10!}{\not 10! ~. ~2!} \\\\\\C_{12}^2 = \dfrac{12 ~. ~11 }{2} \\\\\\C_{12}^2 = \dfrac{132}{2} \\\\\\C_{12}^2 = 66 ~ casos ~ favor\acute{a}veis[/tex]

Casos favoráveis para a peça preta , contar as casas pretas.

[tex]C_{13}^2 = \dfrac{13!}{13! ~. ~2!} \\\\\\C_{13}^2 = \dfrac{11 ~. ~12 ~. 11!}{11! ~. ~2!} \\\\\\C_{13}^2 = \dfrac{13 ~. ~12 ~. \not 11!}{\not 11! ~. ~2!} \\\\\\C_{13}^2 = \dfrac{13 ~. ~12 }{2} \\\\\\C_{13}^2 = \dfrac{156}{2} \\\\\\C_{13}^2 = 78 ~ casos ~ favor\acute{a}veis[/tex]

Somar os casos favoráveis.

[tex]x = 66 + 78\\\\x = 144[/tex]

Dividir os casos possíveis pelos casos favoráveis:

[tex]y = \dfrac{144}{300} \\\\\\y = \dfrac{144 ~\div 12}{300~\div 12} \\\\\\y = \dfrac{12}{25}[/tex]

===

Para saber mais.

https://brainly.com.br/tarefa/46338973

https://brainly.com.br/tarefa/15134199

https://brainly.com.br/tarefa/38860015