Question

Two dice are thrown at a time. What is the probability that the difference of the numbers shown on the dice is $1$ ?

Answer 1

|x-y|=1

if x=1 y=2

if x=2 y=1,2

if x=3 y=2,4

if x=4 y=3,5

if x=5 y=3,5

if x=5 y=4,6

if x=6 y=5

$\therefore$ no of probabilities = 1+2+2+2+2+1=10

$\therefore$ probability=$\frac{no.offavourableoutcomes}{totaloutcomes}$

probability=$\frac{10}{(6\times 6)}=\frac{10}{36}=\frac{5}{18}$

$\therefore$ probability that the difference will be '1' is 5/18