There are $2$ red discs, $6$ green discs and $~1$ blue disc on a table. The discs are identical in a

Question

There are $2$ red discs, $6$ green discs and $~1$ blue disc on a table. The discs are identical in all aspects except colour. The $9$ discs are arranged in a line. Find the number of different possible arrangements such that the $2$ red discs and the blue disc are next to one another. [2] All the $9$ discs are put into a bag. Jack takes $3$ discs from the bag at random. The random variable $R$ is the number of red discs taken. Tabulate the probability distribution of $R$. [3] For each red disc taken, Jack gains nine points. Otherwise, he loses three points for each disc of any other colour taken. Find the expected change in points Jack has after taking the $3$ discs. [3]

Accepted Answer

(a) $21$; (b)(i) $P(R=0)=\frac5{12}$, $P(R=1)=\frac12$, $P(R=2)=\frac1{12}$; (b)(ii) $E(C)=-1$

2023 YIJC P2 Q7

2023 YIJC P2 Q7

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