A bag contains $5$ red balls and $3$ blue balls. In a game, Anne removes balls at random from th

Question

A bag contains $5$ red balls and $3$ blue balls. In a game, Anne removes balls at random from the bag, one at a time, without replacement, until she has taken out $2$ red balls. The total number of balls Anne removes from the bag is denoted by $X$. Find $\mathrm{P}\left( X=x \right)$ for all possible values of $x$.[3] Find $\mathrm{E}\left( X \right)$ and $\mathrm{Var}\left( X \right)$.[3] Anne pays $\$1$ every time she removes a ball and she will receive $\$y$ once she gets $2$ red balls. Calculate the value of $y$ if the game is fair.[2]

Accepted Answer

(i) ${\frac{1}{14}}$ (ii) ${\frac{6}{7}}$ (iii) ${3}$

2023 SAJC P2 Q6

2023 SAJC P2 Q6

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