Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
A fair tetrahedral die has the faces labelled 1, 2, 3, 4. A biased coin has probability \(\frac{1}{3}\) of landing on a head when it is tossed. The die is thrown once and the value \(n\) on the face it lands on is recorded. The biased coin is then tossed \(n\) times. For instance, if the die lands on 3, the coin is tossed 3 times.
(a(i))[3]
Determine the probability that the die shows 4 and the coin produces 2 heads.
(a(ii))[1]
Determine the probability that the die lands on 3 and the coin shows 3 heads.
(a(iii))[3]
Determine the probability that the die lands on the same number as the number of heads shown by the coin.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Multiply their \(2H\) expression by \(\frac14\), for example \(P(4,2H)=\frac14\times{^4C_2}(\frac13)^2(\frac23)^2\)” …