# Easy Probability Solved QuestionAptitude Discussion

 Q. Four dice are thrown simultaneously. Find the probability that all of them show the same face.
 ✔ A. 1/216 ✖ B. 1/36 ✖ C. 4/216 ✖ D. 3/216

Solution:
Option(A) is correct

The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:

$= 6×6×6×6= 6^4$

$n(S)=6^4$

Let $X$ be the event that all dice show the same face.

$X = \{(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)\}$

$n(X)= 6$

Hence required probability,

$= \dfrac{n(X)}{n(S)} = \dfrac{6}{6^4}$

$= \textbf{1/216}$

## (5) Comment(s)

Mervin
()

4 Dice are rolled so $6^4=1296$

faces of all 4 dices must be same so $\dfrac{4}{1296}=\dfrac{1}{324}$

RAKESH
()

Every dice has six faces so we should divide 6 faces with the number of event that is,

$=\dfrac{6}{2196}=\dfrac{1}{216}$

Aniekhan
()

when we multiply 6 four times it comes 1'296 so;how 216 comes ????

RAKESH
()

Four dice are thrown simultaneously so the total number of event is

$=6*6*6*6=1296$

The same face will be obtained for a 6 times,

So, $n(p) = \dfrac{6}{1296}=\dfrac{1}{216}$.

Maninder Singh
()

i hav a question related to partnership

A nad B started a bussiness with investmemnt of rs 45000 and 60000. by mistake they divided the profit in ratio 1:3 and A loses rs 500 .what is the total profit?