Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Maryam has $7$ sweets in a tin, consisting of $6$ toffees and $1$ chocolate. She picks one sweet at random and removes it. Her friend then puts $3$ chocolates into the tin. After that, Maryam selects another sweet at random from the tin.
(i)[3]
Create a fully labelled tree diagram to show this situation.
(ii)[3]
Construct the probability distribution table for the number of toffees taken.
(iii)[1]
Calculate the mean number of toffees taken.
(iv)[4]
Find the probability that the first sweet chosen is a chocolate, given that the second sweet chosen is a toffee.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The initial pair of branches is correct, with probabilities $\frac{6}{7}$ and $\frac{1}{7}$” …