Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
Judy and Steve take part in a game with five cards labelled $3, 4, 5, 8, 9$. Judy first picks one card at random, reads its number and puts the card back. Steve then does the same, choosing a card at random, reading the number and replacing the card. If the two numbers match, the score is $0$. If they are different, the smaller number is taken away from the larger number to give the score.
When the score is $0$, they take another turn. When the score is $4$ or more, Judy wins; otherwise Steve wins. They keep playing until one player wins.
(i)[1]
Show that the probability of obtaining a score of $6$ is $0.08$.
(ii)[2]
Set out a probability distribution table for the score.
(iii)[1]
Calculate the mean value of the score.
(iv)[3]
Find the probability that Judy wins on the second choice of cards.
(v)[2]
Find an expression for the probability that Judy wins on the $n$th choice of cards.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct evaluation $P(6) = P(3,9)+P(9,3) = \frac{2}{25}$” …