Question

Find the probability of getting a sum of the numbers on them is $7$, when two dice are rolled at a time.

• A. $\frac{1}{5}$
• B. $\frac{1}{6}$
• C. $\frac{1}{7}$
• D. $\frac{1}{8}$

Answer 1

Answer: (B)

$\frac{1}{6}$

S is sample space
S= {$(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1)$,
$(2,2),(2,3),(2,4),(2,5),(2,6),(3,1)$
$(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),$
$(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)$,$(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)$}
n(S)= $36$
Let A be the event of getting sum of the numbers on dice be $7$
$\therefore$ A = $(6,1),(1,6),(2,5),(5,2),(3,4),(4,3)$
n(A)= $6$
P(A) = $\frac{n\left(A\right)}{n\left(S\right)}$ = $\frac{6}{36}$
P(A) = $\frac{1}{6}$