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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 :

GinnyAnsweridn
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).
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