Marco has four boxes labelled \(K\), \(L\), \(M\) and \(N\). He places them in a straight line in the order \(K\), \(L\), \(M\), \(N\) with \(K\) on the left. Marco also has four coloured marbles: one is red, one is green, one is white and one is yellow. He places a single marble in each box, at random. Events \(A\) and \(B\) are defined as follows. \(A\): The white marble is in either box \(L\) or box \(M\). \(B\): The red marble is to the left of both the green marble and the yellow marble. Determine whether or not events \(A\) and \(B\) are independent. [3]

Question 5:
5 | Where a candidate has misread a number in the question and used that value consistently throughout, provided that number does not alter the difficulty or
the method required, award all marks earned and deduct just 1 mark for the misread.
5 | 1 8 1
P(A) = , P(B) = = ,
2 24 3 | B1 | Both stated, accept unsimplified.
1
P(AB) =
6 | M1 | Evidence that independence properties not used.
1 1 1
P(A) × P(B) =  =
2 3 6
so events are independent | A1 | Evaluated and conclusion stated.
P(A) × P(B) and P(AB) seen.
3
Question | Answer | Marks | Guidance

Marco has four boxes labelled $K$, $L$, $M$ and $N$. He places them in a straight line in the order $K$, $L$, $M$, $N$ with $K$ on the left. Marco also has four coloured marbles: one is red, one is green, one is white and one is yellow. He places a single marble in each box, at random. Events $A$ and $B$ are defined as follows.

$A$: The white marble is in either box $L$ or box $M$.

$B$: The red marble is to the left of both the green marble and the yellow marble.

Determine whether or not events $A$ and $B$ are independent. [3]

\hfill \mbox{\textit{CAIE S1 2023 Q5 [3]}}