Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
In a television quiz show, Peter tackles questions in order and the game stops immediately once a question is answered incorrectly. The probabilities are: Peter answers correctly himself $0.7$; Peter answers wrongly himself $0.1$; Peter decides to ask for help $0.2$. The first time Peter chooses to ask for help, he asks the audience. The probability that the audience supplies the correct answer is $0.95$.
(i)[1]
Show that the chance that the first question is answered correctly is $0.89$.
(ii)[6]
Find the probability that both of the first two questions are answered correctly.
(iii)[3]
Given that both of the first two questions were answered correctly, find the probability that Peter asked the audience.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Probability for the first correct answer evaluated correctly, e.g. $P(\text{1st correct}) = 0.7 + 0.2 \times 0.95 = 0.89$” …