Probability of outcome from a fair die

A fair die is rolled 5 times:
a) What is probability that an even number is cast at least once?

b) What is probability that a six is cast each time?

Answer

The first probability is $1-(1/2)^5$
The second is $(1/6)^5$

a)
Let A:= "at least one even number is rolled".
Then P(A) = 1 - P(only uneven numbers are rolled) = $1- (1/2)^5$

b) P(roll a six in one try) = 1/6

Therefore P(roll a six 5 times in a row) = $(1/6)^5$ because each rolling the die is independent from the others.