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A farmer grows red and white flowers. In his warehouse, $\frac{1}{12}$ of the white flowers are roses. $\frac{2}{3}$ of the red flowers are roses. $25\%$ of all the flowers are roses. The rest are lily flowers. You randomly chose a flower from the warehouse. What is the probability that the flower is red? What is the probability that he flower is red if it is a rose? Given that the number of roses is $300$, what is the total number of flowers in the warehouse?

We worked out that $\frac{2}{7}$ of the flowers are red. But then we got stuck.

Rick
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Damien Hila Urban
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  • The answer below answers everything except the most basic question you posed: the total number of flowers in the warehouse. We are told that there are $300$ roses, and this is $25%$ of the total flowers. Therefore there are $\frac{100%}{25%}\times300=1200$ flowers in the warehouse. – K.defaoite May 17 '20 at 19:25

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Hint:

If there are $w$ white flowers and $r$ red flowers, then we have $$\frac{w}{12} + \frac{2r}{3} = \frac{w+r}{4} \implies \frac wr =\frac 52$$ Now, $$P(\text{red |rose})=\frac{P(\text{red and rose})}{P(\text{rose})} =\frac{\frac{2r}{3}}{\frac{2r}{3} + \frac{w}{12}} = \frac{\frac 23}{\frac 23 + \frac{1}{12}\cdot \frac wr}$$ $$\cdots$$

Vishu
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