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).
