Question

A farmer has an orchard that covers an area of 40 acres. He grows apples on 25 acres, peaches on 7 acres, nectarines on 5 acres, and plums on 3 acres. The fruit trees are equally distributed within the orchard. A tree is chosen at random. Rounded to the nearest tenth of a percent, what is the theoretical probability that the tree is not within the acres of apple trees?
25.0%
37.5%
62.5%
75.4%

Answer 1

P(!A)=(number of all acres minus apple acres)/(total acres)

P(!A)=(40-25)/40

P(!A)=15/40

P(!A)=3/8 

P(!A)=.375  which is:

P(!A)=100(.375)%

P(!A)=37.5%

Answer 2

Answer:  Second option is correct.

Explanation:

Since we have given that

Total area a farmer has as an orchard = 40 acres

Total area in which he grows apples = 25 acres

Total area on which he grows peaches = 7 acres

Total area on which he grows nectarines = 5 acres

Total area on which he grows plums = 3 acres

According to question, the fruit trees are equally distributed within the orchard,

So,

P( the tree is within the acres of apple trees) is given by

$\frac{\text{ total number of apple trees}}{\text{ Total area}}=\frac{25}{40}=\frac{5}{8}$

But we have to calculate the Probability that the tree is not within the acres of apple trees,

So, P( the tree is not within the acres of apple trees) is given by

$1-\frac{5}{8}=\frac{8-5}{8}=\frac{3}{8}\\\\\implies \frac{3}{8}\times 100=\frac{300}{8}=37.5\%$

Hence, Second option is correct.