Question

A die is thrown twice. What is the probability that:
(i) $3$ will come up either time?
(ii) $3$ will come up atleast once?

Answer 1

$\left(i\right)$ 3 will come up either time

probability of 3 coming up first time is $\frac{1}{6}$

second time is also $\frac{1}{6}$

total probability is $\frac{1}{6}.\frac{1}{6}=\frac{1}{36}$

$\left(ii\right)$ 3 will come up atleast once

either 3 will come up first time or second time or both

so probability is $\frac{1}{6}.\frac{5}{6}+\frac{5}{6}.\frac{1}{6}+\frac{1}{6}.\frac{1}{6}=\frac{11}{36}$