Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Deeti has 3 red pens and 1 blue pen in her left pocket, and her right pocket also contains 3 red pens and 1 blue pen. Operation $T$ means that Deeti first takes one pen at random from her left pocket and puts it into her right pocket, and then takes one pen at random from her right pocket and puts it into her left pocket. The random variable $X$ gives the number of blue pens in Deeti’s left pocket after operation $T$ has been completed.
(i)[2]
Find the probability that, when Deeti carries out operation $T$, she takes a blue pen from her left pocket and then a blue pen from her right pocket.
(ii)[3]
Find the value of $P(X = 1)$.
(iii)[4]
Given that the pen removed from Deeti’s right pocket is blue, find the probability that the pen removed from Deeti’s left pocket is blue.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Calculate the value of $P(B,B)=\frac14\times\frac25$” …