probability

Question

When 4 dice are thrown, what is the probability that the same number appears on each of them?

      a. 1/36           b. 1/18           c. 1/216         d. 1/5

Answer 1

$1,2,\dots,6$ - 6 possibilities for each throw and hence total $6^4$ cases. Only 6 are favorable corresponding to $\langle 1,1,1,1 \rangle, \langle 2,2,2,2 \rangle, \dots, \langle 6,6,6,6 \rangle.$ So, required probability $ = \frac{6}{6^4} = \frac{1}{216}.$

Answer 2

n(s)=6^4=1296

n(e)=(1,1,1,1),(2,2,2,2).......(6,6,6,6)

probability=6/1296

=1/216