Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Nadia is extremely forgetful. Whenever she signs in to her online bank, she has only a $40\%$ chance of typing her password correctly. On any one day, she is permitted $3$ unsuccessful attempts, after which the bank stops her from trying again until the next day.
(i)[3]
Produce a fully annotated tree diagram to show this situation.
(ii)[4]
Let $X$ represent the number of unsuccessful attempts Nadia makes on a day when she tries to sign in to her bank. Copy and finish the table below to show the probability distribution of $X$.
(iii)[2]
Calculate the expected number of unsuccessful attempts Nadia makes on any day when she tries to log in.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Construct a tree diagram using probabilities $0.4$ and $0.6$.” …