Answer :
Let's answer each of the given questions step-by-step.
### Question 1
How many favorable outcomes are expressed in the probability [tex]\(\frac{7}{9}\)[/tex]?
The number of favorable outcomes is represented by the numerator in the probability fraction. Therefore, the number of favorable outcomes is:
[tex]\[ \boxed{7} \][/tex]
### Question 2
How many possible outcomes are expressed in the probability [tex]\(\frac{14}{25}\)[/tex]?
The number of possible outcomes is represented by the denominator in the probability fraction. Therefore, the number of possible outcomes is:
[tex]\[ \boxed{25} \][/tex]
### Question 3
What fraction correctly shows the probability of 14 favorable outcomes out of 21 possible outcomes?
The probability fraction for 14 favorable outcomes out of 21 possible outcomes is:
[tex]\[ \frac{14}{21} \][/tex]
Thus, the correct fraction is:
[tex]\[ \boxed{\frac{14}{21}} \][/tex]
### Question 4
Which probability is least likely: [tex]\(\frac{17}{35}, \frac{5}{13}, \frac{132}{425}, \frac{1}{2}\)[/tex]?
To determine which probability is least likely, we compare the following values:
[tex]\[ \frac{17}{35} \approx 0.486 \][/tex]
[tex]\[ \frac{5}{13} \approx 0.385 \][/tex]
[tex]\[ \frac{132}{425} \approx 0.3106 \][/tex]
[tex]\[ \frac{1}{2} = 0.5 \][/tex]
Among these values, [tex]\(0.3106\)[/tex] is the smallest. Therefore, the least likely probability is:
[tex]\[ \boxed{\frac{132}{425}} \][/tex]
### Question 5
Select the value(s) that could be the probability of an event.
Here are the given values:
- [tex]\(0.5\)[/tex]
- [tex]\(\frac{4}{3}\)[/tex]
- [tex]\(-1\)[/tex]
Probabilities must lie in the range [tex]\([0, 1]\)[/tex]. Therefore, the only value(s) that could be the probability of an event is/are:
[tex]\[ \boxed{0.5} \][/tex]
[tex]\[ \boxed{ } \][/tex]
This completes the solution for the given questions.
### Question 1
How many favorable outcomes are expressed in the probability [tex]\(\frac{7}{9}\)[/tex]?
The number of favorable outcomes is represented by the numerator in the probability fraction. Therefore, the number of favorable outcomes is:
[tex]\[ \boxed{7} \][/tex]
### Question 2
How many possible outcomes are expressed in the probability [tex]\(\frac{14}{25}\)[/tex]?
The number of possible outcomes is represented by the denominator in the probability fraction. Therefore, the number of possible outcomes is:
[tex]\[ \boxed{25} \][/tex]
### Question 3
What fraction correctly shows the probability of 14 favorable outcomes out of 21 possible outcomes?
The probability fraction for 14 favorable outcomes out of 21 possible outcomes is:
[tex]\[ \frac{14}{21} \][/tex]
Thus, the correct fraction is:
[tex]\[ \boxed{\frac{14}{21}} \][/tex]
### Question 4
Which probability is least likely: [tex]\(\frac{17}{35}, \frac{5}{13}, \frac{132}{425}, \frac{1}{2}\)[/tex]?
To determine which probability is least likely, we compare the following values:
[tex]\[ \frac{17}{35} \approx 0.486 \][/tex]
[tex]\[ \frac{5}{13} \approx 0.385 \][/tex]
[tex]\[ \frac{132}{425} \approx 0.3106 \][/tex]
[tex]\[ \frac{1}{2} = 0.5 \][/tex]
Among these values, [tex]\(0.3106\)[/tex] is the smallest. Therefore, the least likely probability is:
[tex]\[ \boxed{\frac{132}{425}} \][/tex]
### Question 5
Select the value(s) that could be the probability of an event.
Here are the given values:
- [tex]\(0.5\)[/tex]
- [tex]\(\frac{4}{3}\)[/tex]
- [tex]\(-1\)[/tex]
Probabilities must lie in the range [tex]\([0, 1]\)[/tex]. Therefore, the only value(s) that could be the probability of an event is/are:
[tex]\[ \boxed{0.5} \][/tex]
[tex]\[ \boxed{ } \][/tex]
This completes the solution for the given questions.
