Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Susan has a bag of sweets with 7 chocolates and 5 toffees inside it. Ahmad has a bag of sweets with 3 chocolates, 4 toffees and 2 boiled sweets inside it. One sweet is selected at random from Susan’s bag and added to Ahmad’s bag. Then one sweet is chosen at random from Ahmad’s bag.
(i)[2]
Determine the probability that the two sweets chosen are a toffee from Susan’s bag and a boiled sweet from Ahmad’s bag.
(ii)[4]
Knowing that the sweet taken from Ahmad’s bag is a chocolate, find the probability that the sweet taken from Susan’s bag was also a chocolate.
(iii)[5]
The random variable $X$ counts the number of times a chocolate is selected. State the possible values of $X$ and produce a table showing the probability distribution of $X$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write $P(T,B)=\frac{5}{12}\times\frac{2}{10}$” …