question help

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hi guys i had a question with question 3bi and ii in the 2012 exam 2 section 2 paper plaz help

[rhinwarr]

They are both Markov chains questions.

Draw up two probability trees.

Correct -> Correct 0.75
Correct -> Incorrect 0.25

Incorrect -> Correct 2/3
Incorrect -> Incorrect 1/3

For question 3bi, you have to follow through the probability trees for each step. There will be two different ways because question 2 can either be correct or incorrect.
So if C means correct and I means incorrect, there will be CCCC and ICCC. Remember, she answers question 1 incorrectly.

So the answer would be:
(2/3 * 0.75 * 0.75 * 0.75) + (1/3 * 2/3 * 0.75 * 0.75)

For question 3bii, you can use transition matrices.
The transition matrix will be:
[0.75   2/3 ]
[0.25   1/3 ]
The initial matrix will be:
[ 0 ]
[ 1 ]
(because she gets the first question incorrect).

Then you do:
Transition matrix ^24 times initial matrix = answer

You choose the answer on the top of the matrix because you are finding the probability that she will get it CORRECT.

Sorry if this is confusing, its hard to type it out :/