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.
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