Question

Three dice are thrown simultaneously. What is the probability of getting a total of atleast $5$ of the numbers on their tops ?

Answer 1

Three dice are thrown simultaeously, total number of outcomes$=6^3=216$

Getting a total of atleast $5$ means $5$ and more than $5$

Now, outcomes with total less than $5=(1,1,1),(1,1,2),(1,2,1),(2,1,1)$

Number of outcomes with total less than $5=4$

Thus, probability of getting a total less than $5=\frac{4}{216}$

Hence, required probability of getting a total of atleast $5$

$=1-P(gettingatotal<5)$

$=1\frac{4}{216}$

$=\frac{216-4}{216}=\frac{212}{216}=\frac{53}{54}$