Let's analyze the probability of choosing a green grape from a bag that contains red and green grapes. Given that the probability [tex]\( P \)[/tex] of choosing a green grape is described by the fraction [tex]\( \frac{11}{15} \)[/tex].
1. First, Convert the Fraction to a Decimal:
To better understand the probability, we convert [tex]\( \frac{11}{15} \)[/tex] to a decimal. This involves dividing the numerator (11) by the denominator (15):
[tex]\[
P = \frac{11}{15} \approx 0.7333333333333333
\][/tex]
2. Classify the Probability:
Next, we need to classify this probability into one of the descriptive terms provided: impossible, unlikely, likely, or certain.
- Impossible: This term is used when the probability is 0. For example, if the event cannot occur at all.
- Unlikely: This term is used when the probability is greater than 0 but less than or equal to 0.25, indicating that the event is not expected to happen often.
- Likely: This term is used when the probability is greater than 0.25 but less than 1, indicating that the event has a good chance of occurring.
- Certain: This term is used when the probability is 1, indicating that the event will definitely occur.
3. Determine the Appropriate Term:
Since [tex]\( 0.7333333333333333 \)[/tex] falls between 0.25 and 1, the best term to describe this probability is likely.
Thus, the probability of choosing a green grape out of the bag of grapes without looking, which is [tex]\( \frac{11}{15} \)[/tex], is likely.
