Answer :
To determine how likely it is to choose a green marble, let’s first understand the given probability and then interpret it in the context of probability theory.
### Step-by-Step Solution:
1. Probability Definition:
- The probability [tex]\( P \)[/tex] of an event quantifies how likely that event is to occur. Probabilities are typically expressed as fractions, decimals, or percentages ranging from 0 to 1 (or 0% to 100%).
2. Given Probability:
- The probability of drawing a green marble is given by [tex]\( P(\text{green}) = \frac{3}{4} \)[/tex].
3. Convert to Decimal/Percentage:
- Converting this fraction to a decimal helps to better understand it.
[tex]\[ P(\text{green}) = \frac{3}{4} = 0.75 \][/tex]
- As a percentage, this would be:
[tex]\[ 0.75 \times 100 = 75\% \][/tex]
4. Interpret the Probability:
- A probability of 0 means the event is impossible.
- A probability of 1 means the event is certain.
- A probability of 0.5 (or 50%) means the event is equally likely and unlikely.
- A probability closer to 1 (but less than 1) indicates a high likelihood but not certainty.
5. Likelihood of Drawing a Green Marble:
- Since [tex]\( P(\text{green}) = 0.75 \)[/tex] (or 75%), it indicates that drawing a green marble is highly likely, though it is not an absolute certainty.
### Conclusion:
- Based on this probability, we can interpret the likelihood of drawing a green marble as very likely.
So, the appropriate choice would be:
- Likely
This means the probability of choosing a green marble is indeed high, indicating that it is very likely but not guaranteed.
### Step-by-Step Solution:
1. Probability Definition:
- The probability [tex]\( P \)[/tex] of an event quantifies how likely that event is to occur. Probabilities are typically expressed as fractions, decimals, or percentages ranging from 0 to 1 (or 0% to 100%).
2. Given Probability:
- The probability of drawing a green marble is given by [tex]\( P(\text{green}) = \frac{3}{4} \)[/tex].
3. Convert to Decimal/Percentage:
- Converting this fraction to a decimal helps to better understand it.
[tex]\[ P(\text{green}) = \frac{3}{4} = 0.75 \][/tex]
- As a percentage, this would be:
[tex]\[ 0.75 \times 100 = 75\% \][/tex]
4. Interpret the Probability:
- A probability of 0 means the event is impossible.
- A probability of 1 means the event is certain.
- A probability of 0.5 (or 50%) means the event is equally likely and unlikely.
- A probability closer to 1 (but less than 1) indicates a high likelihood but not certainty.
5. Likelihood of Drawing a Green Marble:
- Since [tex]\( P(\text{green}) = 0.75 \)[/tex] (or 75%), it indicates that drawing a green marble is highly likely, though it is not an absolute certainty.
### Conclusion:
- Based on this probability, we can interpret the likelihood of drawing a green marble as very likely.
So, the appropriate choice would be:
- Likely
This means the probability of choosing a green marble is indeed high, indicating that it is very likely but not guaranteed.
