Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
Sharik tries an online multiple-choice revision question. There are $3$ suggested answers, and exactly one is correct. When Sharik selects an answer, the computer shows whether it is right or wrong. First, Sharik picks one of the three suggested answers at random. If that choice is wrong, he gets a second attempt by selecting at random from the other $2$. If that too is wrong, Sharik then selects the last remaining answer, which has to be correct.
(i)[4]
Draw a fully labelled tree diagram to show the different choices Sharik can make until the computer shows that he has answered the question correctly.
(ii)[4]
The random variable $X$ is the number of attempts Sharik makes up to and including the one that the computer shows is correct. Construct the probability distribution table for $X$ and find $\text{E}(X)$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Tree has the correct form with the right number of branches” …