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

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.

Answer 2

Probability is the chance of an event occurring. The theoretical probability that the tree is not within the acres of apple trees is 0.375(37.5%).

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

Given to us

Area of orchard = 40 acres

The area that has apple = 25 acres

The area that has peaches= 7 acres

The area that has nectarines = 5 acres

The area that has pulm = 3 acres

We know that probability is the ratio of the desired outcome to the total possible outcomes. therefore, the probability of choosing an apple tree,

Probability = Desired Outcome / Total possible outcome

Choosing an apple tree,

Probability(Apple)

= Area that contains apple tree/ Total area of the Orchard

= 25 / 40

= 0.625

We know that the sum of all the probabilities of an event is 1. And the probability of choosing an apple tree is 0.625.

Probability(Not choosing apple tree) = 1 - Probability(choosing apple tree)

Probability(Not choosing apple tree) = 1- 0.625

Probability(Not choosing apple tree) = 0.375

Probability(Not choosing apple tree) = 37.5%

Hence, the theoretical probability that the tree is not within the acres of apple trees is 0.375(37.5%).

Learn more about Probability:

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