Question

Two dice were thrown simultaneously. Then find the probability of getting difference of outcomes as 2.

• A. $\frac{2}{9}$
• B. $\frac{1}{9}$
• C. $\frac{5}{12}$
• D. $\frac{5}{18}$

Answer 1

The correct option is A $\frac{2}{9}$

The total possible outcomes will be $6\times 6=36$
They are :
$(1,1),(2,1),(3,1),(4,1),(5,1),(6,1),$
$(1,2),(2,2),(3,2),(4,2),(5,2),(6,2),$
$(1,3),(2,3),(3,3),(4,3),(5,3),(6,3),$

$(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),$
$(1,5),(2,5),(3,5),(4,5),(5,5),(6,5),$
$(1,6),(2,6),(3,6),(4,6),(5,6),(6,6)$

Number of getting difference of outcomes as 2, $=8$
[i.e.$(1,3)(2,4)(3,5)(4,2)(4,6)(5,3)(6,4)$]

$P\left(A\right)=\frac{Numberoffavorableoutcomes}{TotalNumberofpossibleoutcomes}$
Probability $P$ $=\frac{8}{36}=\frac{2}{9}$

hence, option $A$ is correct.