Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
In a game, Jim throws three darts at a board; this counts as one ‘turn’. The board’s centre is known as the bull’s-eye. Let the random variable $X$ represent how many darts in a turn land on the bull’s-eye. The probability distribution of $X$ is shown in the table below: $x = 0, 1, 2, 3$ with $P(X = x) = 0.6, p, q, 0.05$. You are told that $\text{E}(X) = 0.55$.
(a)[4]
Find the values of $p$ and $q$ from the information given.
(b)[2]
Find $\mathrm{Var}(X)$ using the given information.
(c)[3]
Find the probability that $X=1$ occurs in at least $3$ of $12$ randomly chosen turns.
(d)[1]
Find the probability that Jim first succeeds in hitting the bull’s-eye with all three darts on his $9\text{th}$ turn.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct probability equations, for example $p+q+0.65=1$.” …