Question

Qual a probabilidade de lançar um dado e obter um número par ou múltiplo de 3?.

Answer 1

$\large\boxed{\begin{array}{l}\sf A\longrightarrow evento\,"sair\,n\acute umero\,par"\\\sf B\longrightarrow evento"sair\,m\acute ultiplo\,de\,3"\\\sf A=\{2,4,6\}\implies n(A)=3\\\sf B=\{3,6\}\implies n(B)=2\\\sf A\cap B=\{6\}\implies n(A\cap B)=1\\\sf U=\{1,2,3,4,5,6\}\implies n(U)=6\\\sf P(A)=\dfrac{n(A)}{n(U)}=\dfrac{3}{6}\\\\\sf P(B)=\dfrac{2}{6}\\\\\sf P(A\cap B)=\dfrac{1}{6}\\\\\sf P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\sf P(A\cup B)=\dfrac{3}{6}+\dfrac{2}{6}-\dfrac{1}{6}\end{array}}$

$\large\boxed{\begin{array}{l}\sf P(A\cup B)=\dfrac{4\div2}{6\div2}\\\\\sf P(A\cup B)=\dfrac{2}{3}(\red{\tt resposta})\end{array}}$