(a)[1]
State the mean of $X$.
(b)[2]
Find the probability that a 5 is first obtained after the $3\text{rd}$ throw but before the $8\text{th}$ throw.
(c)[2]
Find the probability that a 5 is first obtained in fewer than $10$ throws.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
An ordinary fair die is thrown again and again until a 5 appears. Let the random variable $X$ represent the number of throws needed.