Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
Sam belongs to a soccer club and is practising how to score goals. On each attempt, the probability that Sam scores a goal is $0.7$, independent of every other attempt.
(a)[3]
Sam takes 10 shots at goal. Find the probability that Sam will score on fewer than 8 of these attempts.
(b)[2]
Find the probability that Sam’s first successful attempt occurs before her 5th attempt.
(c)[3]
Wei is also a member of the same soccer club, and he is practising scoring goals too. The probability that Wei will score a goal on any attempt is $0.6$, independent of every other attempt. Wei will continue making attempts until he has scored $3$ goals. Find the probability that his third goal is scored on his $7$th attempt.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sets up the binomial probability, for example $P(X<8)=1-[P(X=8)+P(X=9)+P(X=10)]$, with $X\sim B(10,0.7)$ (or an equivalent method).” …