Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
The Notes and the Classics are competing in a choir contest. A sizeable crowd is watching. 30% of the crowd support the Notes. 45% support the Classics. Everyone else backs neither choir. Nobody in the crowd supports both choirs.
(i(a))[3]
From the audience, take a random sample of 6 people. Determine the probability that at most 2 of the 6 people are Notes supporters.
(i(b))[2]
Determine the probability that none of the 6 people support either choir.
(ii)[5]
A random sample of 240 people is selected from the audience. Use an appropriate approximation to find the probability that fewer than 50 do not support either choir.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate binomial probability use, for example ${}^6C_k 0.3^k 0.7^{6-k}$ for $k=0,1,2$” …