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Sagot :
Alright, let's solve this question step-by-step.
1. Items in the bag:
- There are a total of 2 baseballs (B), 5 tennis balls (T), and 3 whiffle balls (W).
- The total number of balls is [tex]\(2 + 5 + 3 = 10\)[/tex].
2. Probability of pulling out a baseball:
- Reduced Fraction:
The probability (P) of pulling out a baseball is given by the ratio of the number of baseballs to the total number of balls.
[tex]\( P(B) = \frac{\text{Number of baseballs}}{\text{Total number of balls}} = \frac{2}{10} = \frac{1}{5} \)[/tex]
- Decimal:
To convert this fraction to a decimal, divide the numerator by the denominator:
[tex]\( P(B) = 0.2 \)[/tex]
- Percent:
To convert the decimal to a percentage, multiply by 100:
[tex]\( P(B) = 0.2 \times 100 = 20\% \)[/tex]
Therefore, [tex]\( P(B) = \frac{1}{5} \text{ (reduced fraction)} = 0.2 \text{ (decimal)} = 20\% \)[/tex].
3. Type of probability:
- This is an example of theoretical probability as we are calculating probabilities based on the known quantities of the different types of balls.
4. Sample space:
- The sample space includes all possible outcomes. Since there are 10 balls in total, the number of outcomes in the sample space is 10.
- Outcomes [tex]\( = 10 \)[/tex].
5. Choosing a baseball:
- In this context, the event or outcome is defined as selecting a baseball from the sample space.
- Therefore, "choosing a baseball" is the outcome we are looking at.
6. Probability of pulling out a tennis ball:
- Reduced Fraction:
The probability (P) of pulling out a tennis ball is given by the ratio of the number of tennis balls to the total number of balls.
[tex]\( P(T) = \frac{\text{Number of tennis balls}}{\text{Total number of balls}} = \frac{5}{10} = \frac{1}{2} \)[/tex]
- Decimal:
To convert this fraction to a decimal, divide the numerator by the denominator:
[tex]\( P(T) = 0.5 \)[/tex]
- Percent:
To convert the decimal to a percentage, multiply by 100:
[tex]\( P(T) = 0.5 \times 100 = 50\% \)[/tex]
Therefore, [tex]\( P(T) = \frac{1}{2} \text{ (reduced fraction)} = 0.5 \text{ (decimal)} = 50\% \)[/tex].
7. More likely outcome:
- To determine which outcome is more likely, compare the probabilities:
[tex]\( P(B) = 20\% \)[/tex]
[tex]\( P(T) = 50\% \)[/tex]
- Since 50% is greater than 20%, pulling out a tennis ball is more likely to occur than pulling out a baseball.
- Therefore, the more likely event is [tex]\( \text{tennis} \)[/tex].
8. Reason:
- This is because the probability of pulling out a tennis ball (50%) is higher than the probability of pulling out a baseball (20%).
So, the completed answer is:
A bag has 2 baseballs (B), 5 tennis balls (T), and 3 whiffle balls (W)
What is the probability of pulling out a baseball? Enter your answers in this order: reduced fraction, decimal, and then percent.
[tex]$ P(B)=1 / 5 \text { (reduced fraction) }=0.2 \text { (decimal) }=20 \% $[/tex]
This is an example of [tex]$\text{theoretical}$[/tex] probability.
How many outcomes are in the sample space? Outcomes [tex]$=$[/tex]
10
In this case, choosing a baseball is the outcome [tex]$\text{desired}$[/tex].
What is the probability of pulling out a tennis ball?
[tex]$ P(T)=1 / 2 \text { (reduced fraction) } 0.5 \text { (decimal) }=50 \% $[/tex]
Which is more likely to occur? [tex]$\text{tennis}$[/tex]
Why? [tex]$\text{Because the probability of pulling a tennis ball is higher.}$[/tex]
1. Items in the bag:
- There are a total of 2 baseballs (B), 5 tennis balls (T), and 3 whiffle balls (W).
- The total number of balls is [tex]\(2 + 5 + 3 = 10\)[/tex].
2. Probability of pulling out a baseball:
- Reduced Fraction:
The probability (P) of pulling out a baseball is given by the ratio of the number of baseballs to the total number of balls.
[tex]\( P(B) = \frac{\text{Number of baseballs}}{\text{Total number of balls}} = \frac{2}{10} = \frac{1}{5} \)[/tex]
- Decimal:
To convert this fraction to a decimal, divide the numerator by the denominator:
[tex]\( P(B) = 0.2 \)[/tex]
- Percent:
To convert the decimal to a percentage, multiply by 100:
[tex]\( P(B) = 0.2 \times 100 = 20\% \)[/tex]
Therefore, [tex]\( P(B) = \frac{1}{5} \text{ (reduced fraction)} = 0.2 \text{ (decimal)} = 20\% \)[/tex].
3. Type of probability:
- This is an example of theoretical probability as we are calculating probabilities based on the known quantities of the different types of balls.
4. Sample space:
- The sample space includes all possible outcomes. Since there are 10 balls in total, the number of outcomes in the sample space is 10.
- Outcomes [tex]\( = 10 \)[/tex].
5. Choosing a baseball:
- In this context, the event or outcome is defined as selecting a baseball from the sample space.
- Therefore, "choosing a baseball" is the outcome we are looking at.
6. Probability of pulling out a tennis ball:
- Reduced Fraction:
The probability (P) of pulling out a tennis ball is given by the ratio of the number of tennis balls to the total number of balls.
[tex]\( P(T) = \frac{\text{Number of tennis balls}}{\text{Total number of balls}} = \frac{5}{10} = \frac{1}{2} \)[/tex]
- Decimal:
To convert this fraction to a decimal, divide the numerator by the denominator:
[tex]\( P(T) = 0.5 \)[/tex]
- Percent:
To convert the decimal to a percentage, multiply by 100:
[tex]\( P(T) = 0.5 \times 100 = 50\% \)[/tex]
Therefore, [tex]\( P(T) = \frac{1}{2} \text{ (reduced fraction)} = 0.5 \text{ (decimal)} = 50\% \)[/tex].
7. More likely outcome:
- To determine which outcome is more likely, compare the probabilities:
[tex]\( P(B) = 20\% \)[/tex]
[tex]\( P(T) = 50\% \)[/tex]
- Since 50% is greater than 20%, pulling out a tennis ball is more likely to occur than pulling out a baseball.
- Therefore, the more likely event is [tex]\( \text{tennis} \)[/tex].
8. Reason:
- This is because the probability of pulling out a tennis ball (50%) is higher than the probability of pulling out a baseball (20%).
So, the completed answer is:
A bag has 2 baseballs (B), 5 tennis balls (T), and 3 whiffle balls (W)
What is the probability of pulling out a baseball? Enter your answers in this order: reduced fraction, decimal, and then percent.
[tex]$ P(B)=1 / 5 \text { (reduced fraction) }=0.2 \text { (decimal) }=20 \% $[/tex]
This is an example of [tex]$\text{theoretical}$[/tex] probability.
How many outcomes are in the sample space? Outcomes [tex]$=$[/tex]
10
In this case, choosing a baseball is the outcome [tex]$\text{desired}$[/tex].
What is the probability of pulling out a tennis ball?
[tex]$ P(T)=1 / 2 \text { (reduced fraction) } 0.5 \text { (decimal) }=50 \% $[/tex]
Which is more likely to occur? [tex]$\text{tennis}$[/tex]
Why? [tex]$\text{Because the probability of pulling a tennis ball is higher.}$[/tex]
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