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- Feb 14, 2012

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A farmer plants 3 types of blueberries, namely highbush, lowbush and hybrid half-high in the ratio 5:3:2. The yield of large blueberries among the types are 30% for highbush, 40% for lowbush and 60% for hybrid half-high. It is found that opossums eat 5% of highbush blueberries, 10% of lowbush blueberries and 20% of hybrid half-high blueberries. Is there any evidence to show that opossums prefer small blueberries?

Attempt:

First, I find the percentage of the large blueberries are eaten by the opossums as follows:

P(large blueberries are eaten by the opossums)

=P(L | E)

$\displaystyle =\frac{(0.5 \times 0.3 \times 0.05)+(0.3 \times 0.4 \times 0.1)+(0.2 \times 0.6 \times 0.2)}{(0.5 \times 0.05)+(0.3 \times 0.1)+(0.2 \times 0.2)} \times 100\%$

$\displaystyle =\frac{0.0435}{0.095} \times 100\%$

$\displaystyle =45.8\%$

Second, I get the percentage of the small blueberries that are eaten by the opossums as 100%-45.8%=54.2%.

Therefore, we can say that there is enough evidence to show that opossums prefer small blueberries because the percentage that we obtained for the small blueberries that are eaten by the opossums is 54.2%, which is more than 50%.

Can someone please tell me is my working valid?

Thanks in advance.