Question

A pair of dice is rolled, Find the probability that sum of numbers appearing on the uppermost faces of the dice is
(i) Greater than 7
(ii) Perfect square
(iii) is 10

Answer 1

A pair of dice is rolled.

Total out comes = $36$

(I) Sum of numbers on upper forces is greater then $7$.

$\Rightarrow sum=8,9,10,11$ or $11$

$\Rightarrow$ Possible out comes are :

$(2,6),(3,5),(4,4),(5,3)$ and $(6,2)\to 8$

$(3,6),(4,5),(5,4),(6,3)\to 9$

$(4,6),(5,5),(6,4)/(5,6),(6,5)\to 10/11$

$(6,6)\to 12$

$\Rightarrow$ Favorable outcomes = $15$

$\Rightarrow$ Probability = $\frac{15}{36}=\frac{5}{12}$

(II) sum = Perfect square = $4,9$

$\Rightarrow$ Favorable are : $(1,3),(2,2),(3,1),(3,6),\left(45\right),(5,4),(6,3)$ Total = $7$

$\Rightarrow P=\frac{7}{36}$

(III) Sum = $10$

$\Rightarrow$ out comes are : $(4,6),(5,5)$ and $6,4)$

$P=\frac{3}{36}=\frac{1}{12}$