Question

No lançamento de dois dados, o espaço amostral pode ser de que forma?
Complete a tabela a baixo e em seguida responda:

Sendo P(s) a probabilidade de a soma dos pontos ser igual a s, obtenha P(5), P(7) e
P(9). (Considere que os dois dados sejam honestos)

Answer 1

Explicação passo-a-passo:

Para cada lançamento há 6 possibilidades. São $\sf 6\cdot6=36$ possibilidades.

O espaço amostral é 36. Podemos representá-lo utilizando pares ordenados.

$\sf \Omega=\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),$

$\sf ~~~~~~~~~~(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),$

$\sf ~~~~~~~~~~(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),$

$\sf ~~~~~~~~~~(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),$

$\sf ~~~~~~~~~~(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),$

$\sf ~~~~~~~~~~(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$

$\sf ~~~~~~~\Big|~~1~~\Big|~~2~~\Big|~~3~~\Big|~~4~~\Big|~~5~~\Big|~~6~~\Big|$

$\sf \Big|~~1~~\Big|~~2~~\Big|~~3~~\Big|~~4~~\Big|~~5~~\Big|~~6~~\Big|~~7~~\Big|$

$\sf \Big|~~2~~\Big|~~3~~\Big|~~4~~\Big|~~5~~\Big|~~6~~\Big|~~7~~\Big|~~8~~\Big|$

$\sf \Big|~~3~~\Big|~~4~~\Big|~~5~~\Big|~~6~~\Big|~~7~~\Big|~~8~~\Big|~~9~~\Big|$

$\sf \Big|~~4~~\Big|~~5~~\Big|~~6~~\Big|~~7~~\Big|~~8~~\Big|~~9~~\Big|~10~\Big|$

$\sf \Big|~~5~~\Big|~~6~~\Big|~~7~~\Big|~~8~~\Big|~~9~~\Big|~10~\Big|~11~\Big|$

$\sf \Big|~~6~~\Big|~~7~~\Big|~~8~~\Big|~~9~~\Big|~10~\Big|~11~\Big|~12~\Big|$

=> P(5)

A soma é 5 nos casos: $\sf (1,4),(2,3),(3,2),(4,1)$.

Temos 4 casos favoráveis e 36 casos possíveis.

Logo:

$\sf P(5)=\dfrac{4}{36}$

$\sf P(5)=\red{\dfrac{1}{9}}$

=> P(7)

A soma é 7 nos casos: $\sf (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$.

Temos 6 casos favoráveis e 36 casos possíveis.

Logo:

$\sf P(7)=\dfrac{6}{36}$

$\sf P(7)=\red{\dfrac{1}{6}}$

=> P(9)

A soma é 9 nos casos: $\sf (3,6),(4,5),(5,4),(6,3)$.

Temos 4 casos favoráveis e 36 casos possíveis.

Logo:

$\sf P(9)=\dfrac{4}{36}$

$\sf P(9)=\red{\dfrac{1}{9}}$