Maths a level probability question

In a game show, each contestant is asked a number of questions. Each question has a choice of three possible answers.
The probability that John knows the answer to any given question is 2/5
If John doesn’t know the answer he guesses. The probability that he guesses correctly is 1/3
Calculate the probability that John answers two consecutive random questions correctly

My understanding is that i should calculate the probabilities by finding
P(knows, doesn't know guesses)
P(doesn't know guesses, knows)
P(knows, knows)
P(doesn't know guesses, doesn't know guesses)
and then add them all up to get 0.36, however the markscheme simply does (0.6)^2
I think i've made it too complicated and any explanation of the answer would be really appreciated

Reply 1

mqb2766

It would be a bit easier to work out the probability of being right each time. Can you see how its 0.6?

Reply 2

mqb2766

Original post by PeaceMinusOne

As far as I know you didn't exactly over complicate it, more like the markscheme left a lot of working out.
Here is my working (excuse the lack of mathemetical notation):
Here you can see that the probability of getting 2 questions correct is 0.6^2.
Hope this helps.

Could you pls delete and have a read of the sticky at the top of the forum about providing hints, rather than solutions. Thanks.

Reply 3

PeaceMinusOne

Original post by mqb2766

Could you pls delete and have a read of the sticky at the top of the forum about providing hints, rather than solutions. Thanks.

My bad, the original person did get to the correct answer and I was just providing a solution which reiterated what they thought.

Thanks

Reply 4

mqb2766

Original post by PeaceMinusOne

My bad, the original person did get to the correct answer and I was just providing a solution which reiterated what they thought.

Thanks

No problem and thanks. The aim is to try and give hints which allow them to do as much as possible themselves.
They've obviously got some idea as they got the joint correct, and thats the product (independent) of p(being right), which is what we're both talking about.