Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
In a game, a player tries to score by sending a ball into the net. The probability that Leno scores a goal is $0.4$ on any attempt, independently of all other attempts. The random variable $X$ represents how many attempts Leno needs before he scores a goal.
(a)[1]
Calculate $P(X = 5)$.
(b)[2]
Calculate $P(3 \leq X \leq 7)$.
(c)[3]
Calculate the probability that Leno scores his second goal on or before his 5th attempt.
(d)[5]
Use a suitable approximation to calculate the probability that Leno scores more than $28$ goals but fewer than $35$ goals.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “So $(0.6)^4\times0.4=0.05184$ or $\frac{162}{3125}$.” …