A bag contains $6$ red counters and $3$ yellow counters. In a game, Cudds remove counters at ran

Question

A bag contains $6$ red counters and $3$ yellow counters. In a game, Cudds remove counters at random from the bag, one at a time, until he has taken out $2$ red counters. The total number of counters Cudds removes from the bag is denoted by $T$. Find $\mathrm{P}\left( T=t \right)$ for all possible values of $t$.[3] Find $\mathrm{E}\left( T \right)$ and $\mathrm{Var}\left( T \right)$.[2] Lee plays this game $15$ times. Find the probability that Lee has to take at least $4$ counters out of the bag in at least $5$ of his $15$ games.[2]

Accepted Answer

(i) $	ext{P}\left( T=2 ight)=\frac{5}{12}$, $	ext{P}\left( T=3 ight)=\frac{5}{14}$, $	ext{P}\left( T=4 ight)=\frac{5}{28}$, $	ext{P}\left( T=5 ight)=\frac{1}{21}$ (ii) $\frac{20}{7}$, $\frac{75}{98}$ (iii) $0.238$ ($3$ s.f.)

N2017 P2 Q5

N2017 P2 Q5

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