Question

Two dice each with faces marked $1,2,3,4,5,6$ are thrown simultaneously. Find the probability of the following events:
(i) The sum of the numbers coming up $7$.
(ii) The sum of the numbers coming up is a multiple of $4$.

• A. $\left(i\right)\frac{1}{6},\left(ii\right)\frac{1}{4}$
• B. $\left(i\right)\frac{1}{3},\left(ii\right)\frac{2}{9}$
• C. $\left(i\right)\frac{5}{6},\left(ii\right)\frac{1}{9}$
• D. None of these
  

Answer 1

Answer: (A)

$\left(i\right)\frac{1}{6},\left(ii\right)\frac{1}{4}$

$n\left(s\right)=6\times 6=36$

i) $E_1=\{(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\}$

$\Rightarrow n\left(E_1\right)=6$

$\therefore$ probability of getting sum of $7=\frac{6}{36}=\frac{1}{6}$

ii) $E_2=\{(1,3),(3,1),(2,6),(6,2),(3,5),(5,3),(4,4),(6,6)\},(2,2)$

$n\left(E_2\right)=9$

$\therefore P\left(E_2\right)=\frac{9}{36}=\frac{1}{4}$