Question

When a six faced dice is rolled the probability that the top face number is a perfect square and also a perfect cube is 

A) 1/6 

B) 1/4 

C) 1/3 

D) 2/3

Answer 1

Correct option is (A) 1/6

Possible outcomes are S = {1, 2, 3, 4, 5, 6}

\(\therefore\) n(S) = 6

Number which is a perfect square and a perfect cube is 1.    \((\because1^3=1\;\&\;1^2=1)\)

Hence, favourable outcome is n(E) = 1

\(\therefore\) Required probability is P(E) \(=\frac{n(E)}{n(S)}=\frac16.\)

Answer 2

Correct option is  A) 1/6