A bag contains $r$ red counters and $b$ blue counters, where $r 12$ and $b 12$. Mei randomly rem

Question

A bag contains $r$ red counters and $b$ blue counters, where $r > 12$ and $b > 12$. Mei randomly removes $12$ counters from the bag. The probability that there are $4$ red counters among Mei's $12$ counters is the same as the probability that there are $3$ red counters. Show that $9r+5=4b$. [2] The probability that there are $3$ red counters among Mei's $12$ counters is $\frac{5}{3}$ times the probability that there are $2$ red counters. Derive an equation similar to the equation in part (a) and hence find the probability that just one of the $12$ counters removed is red. [6]

Accepted Answer

(b) $0.0516$

N2023 P2 Q6

N2023 P2 Q6

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