Question

Two dice were thrown simultaneously. Then find the probability of getting one odd and one even outcome

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{9}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B $\frac{1}{2}$

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 one odd and one even number $=18$
[i.e. $(1,2)(1,4)(1,6)(2,1)(2,3)(2,5)(3,2)(3,4)(3,6)(4,1)(4,3)(4,5)(5,2)(5,4)(5,6)(6,1)(6,3)(6,5)$]

$P\left(A\right)=\frac{Numberoffavorableoutcomes}{TotalNumberofpossibleoutcomes}$
Probability $P\left(A\right)=\frac{18}{36}=\frac{1}{2}$

hence, option $B$ is correct.