Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

A bag has 5 apples, 10 oranges, and 5 peaches.

1. What is the probability of pulling out an apple? Enter your answers in this order: reduced fraction, decimal, and then percent.

[tex]\[
P(A) = \frac{5}{20} = \frac{1}{4}
\][/tex]

[tex]\[
\text{Decimal} = 0.25
\][/tex]

[tex]\[
\text{Percent} = 25\%
\][/tex]

2. What is the probability of pulling out an orange?

[tex]\[
P(O) = \frac{10}{20} = \frac{1}{2}
\][/tex]

[tex]\[
\text{Decimal} = 0.5
\][/tex]

[tex]\[
\text{Percent} = 50\%
\][/tex]

3. Which is more likely to occur: pulling out an apple or pulling out an orange? Explain why.

[tex]\[
\text{Pulling out an orange is more likely because the probability of } P(O) = 0.5 \text{ is closer to 1.}
\][/tex]

Sagot :

GinnyAnswer
Let's solve the problem step by step.

### Given:
- There are 5 apples, 10 oranges, and 5 peaches in a bag.

### 1. Calculate the Total Number of Fruits:
Total fruits [tex]\( T = 5 \)[/tex] apples [tex]\( + 10 \)[/tex] oranges [tex]\( + 5 \)[/tex] peaches [tex]\( = 20 \)[/tex] fruits.

### 2. Probability of Pulling Out an Apple:
To find the probability of pulling out an apple, we use the formula:
[tex]\[ P(A) = \frac{\text{Number of apples}}{\text{Total number of fruits}}. \][/tex]

- Reduced Fraction:
Number of apples [tex]\( = 5 \)[/tex]
Total number of fruits [tex]\( = 20 \)[/tex]
[tex]\[ \text{Reduced Fraction} = \frac{5}{20} = \frac{1}{4} \][/tex]

- Decimal:
[tex]\[ \frac{1}{4} = 0.25 \][/tex]

- Percent:
To convert the decimal to a percent, multiply by 100:
[tex]\[ 0.25 \times 100 = 25\% \][/tex]

So, we have:
[tex]\[ P(A) = \left(\frac{1}{4}, 0.25, 25\%\right) \][/tex]

### 3. Sample Space:
The sample space [tex]\( S \)[/tex] consists of all the types of fruits in the bag, which are apples, oranges, and peaches.
[tex]\[ S = \{ \text{apple}, \text{orange}, \text{peach} \} \][/tex]

### 4. Event Definition:
In this case, the "event" is pulling out an apple.

### 5. Probability of Pulling Out an Orange:
Similarly, to find the probability of pulling out an orange, we use the formula:
[tex]\[ P(O) = \frac{\text{Number of oranges}}{\text{Total number of fruits}}. \][/tex]

- Reduced Fraction:
Number of oranges [tex]\( = 10 \)[/tex]
Total number of fruits [tex]\( = 20 \)[/tex]
[tex]\[ \text{Reduced Fraction} = \frac{10}{20} = \frac{1}{2} \][/tex]

- Decimal:
[tex]\[ \frac{1}{2} = 0.5 \][/tex]

- Percent:
To convert the decimal to a percent, multiply by 100:
[tex]\[ 0.5 \times 100 = 50\% \][/tex]

So, we have:
[tex]\[ P(O) = \left(\frac{1}{2}, 0.5, 50\%\right) \][/tex]

### 6. Comparison:
Finally, comparing the probabilities:
- Probability of pulling out an apple [tex]\( = 0.25 \)[/tex]
- Probability of pulling out an orange [tex]\( = 0.5 \)[/tex]

Since 0.5 is greater than 0.25, pulling out an orange is more likely to occur.

### Conclusion:
- Reduced Fraction, Decimal, and Percent for Apple:
[tex]\[ P(A) = \left(\frac{1}{4}, 0.25, 25\%\right) \][/tex]

- Reduced Fraction, Decimal, and Percent for Orange:
[tex]\[ P(O) = \left(\frac{1}{2}, 0.5, 50\%\right) \][/tex]

- More Likely Event: Pulling out an orange.
- Why: Because the probability of pulling out an orange (0.5) is closer to 1 than the probability of pulling out an apple (0.25).
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.