Answer :
Let's find the probability for each of the following events, step-by-step, based on the survey data provided.
### Probability that the person is female
The total number of people surveyed is 100, out of which the number of females is 44. The probability (P) that a randomly selected person is female is given by:
[tex]\[ P(\text{Female}) = \frac{\text{Number of females}}{\text{Total number of people}} = \frac{44}{100} = 0.44 \][/tex]
### Probability that the person is male
Similarly, the number of males is 56. The probability that a randomly selected person is male:
[tex]\[ P(\text{Male}) = \frac{\text{Number of males}}{\text{Total number of people}} = \frac{56}{100} = 0.56 \][/tex]
### Probability that the person has a college degree
The total number of people with a college degree is 50. The probability that a randomly selected person has a college degree:
[tex]\[ P(\text{College Degree}) = \frac{\text{Number of people with college degree}}{\text{Total number of people}} = \frac{50}{100} = 0.5 \][/tex]
### Probability that the person does not have a college degree
The number of people without a college degree is also 50. The probability that a randomly selected person does not have a college degree:
[tex]\[ P(\text{No College Degree}) = \frac{\text{Number of people without college degree}}{\text{Total number of people}} = \frac{50}{100} = 0.5 \][/tex]
### Probability that the person is a female with a college degree
The number of females with a college degree is 29. The probability that a randomly selected person is a female with a college degree:
[tex]\[ P(\text{Female and College Degree}) = \frac{\text{Number of females with college degree}}{\text{Total number of people}} = \frac{29}{100} = 0.29 \][/tex]
### Probability that the person is a male with a college degree
The number of males with a college degree is 21. The probability that a randomly selected person is a male with a college degree:
[tex]\[ P(\text{Male and College Degree}) = \frac{\text{Number of males with college degree}}{\text{Total number of people}} = \frac{21}{100} = 0.21 \][/tex]
### Probability that the person is a female without a college degree
The number of females without a college degree is 15. The probability that a randomly selected person is a female without a college degree:
[tex]\[ P(\text{Female and No College Degree}) = \frac{\text{Number of females without college degree}}{\text{Total number of people}} = \frac{15}{100} = 0.15 \][/tex]
### Probability that the person is a male without a college degree
The number of males without a college degree is 35. The probability that a randomly selected person is a male without a college degree:
[tex]\[ P(\text{Male and No College Degree}) = \frac{\text{Number of males without college degree}}{\text{Total number of people}} = \frac{35}{100} = 0.35 \][/tex]
Therefore, the probabilities are:
- Probability of selecting a female: 0.44
- Probability of selecting a male: 0.56
- Probability of selecting a person with a college degree: 0.5
- Probability of selecting a person without a college degree: 0.5
- Probability of selecting a female with a college degree: 0.29
- Probability of selecting a male with a college degree: 0.21
- Probability of selecting a female without a college degree: 0.15
- Probability of selecting a male without a college degree: 0.35
### Probability that the person is female
The total number of people surveyed is 100, out of which the number of females is 44. The probability (P) that a randomly selected person is female is given by:
[tex]\[ P(\text{Female}) = \frac{\text{Number of females}}{\text{Total number of people}} = \frac{44}{100} = 0.44 \][/tex]
### Probability that the person is male
Similarly, the number of males is 56. The probability that a randomly selected person is male:
[tex]\[ P(\text{Male}) = \frac{\text{Number of males}}{\text{Total number of people}} = \frac{56}{100} = 0.56 \][/tex]
### Probability that the person has a college degree
The total number of people with a college degree is 50. The probability that a randomly selected person has a college degree:
[tex]\[ P(\text{College Degree}) = \frac{\text{Number of people with college degree}}{\text{Total number of people}} = \frac{50}{100} = 0.5 \][/tex]
### Probability that the person does not have a college degree
The number of people without a college degree is also 50. The probability that a randomly selected person does not have a college degree:
[tex]\[ P(\text{No College Degree}) = \frac{\text{Number of people without college degree}}{\text{Total number of people}} = \frac{50}{100} = 0.5 \][/tex]
### Probability that the person is a female with a college degree
The number of females with a college degree is 29. The probability that a randomly selected person is a female with a college degree:
[tex]\[ P(\text{Female and College Degree}) = \frac{\text{Number of females with college degree}}{\text{Total number of people}} = \frac{29}{100} = 0.29 \][/tex]
### Probability that the person is a male with a college degree
The number of males with a college degree is 21. The probability that a randomly selected person is a male with a college degree:
[tex]\[ P(\text{Male and College Degree}) = \frac{\text{Number of males with college degree}}{\text{Total number of people}} = \frac{21}{100} = 0.21 \][/tex]
### Probability that the person is a female without a college degree
The number of females without a college degree is 15. The probability that a randomly selected person is a female without a college degree:
[tex]\[ P(\text{Female and No College Degree}) = \frac{\text{Number of females without college degree}}{\text{Total number of people}} = \frac{15}{100} = 0.15 \][/tex]
### Probability that the person is a male without a college degree
The number of males without a college degree is 35. The probability that a randomly selected person is a male without a college degree:
[tex]\[ P(\text{Male and No College Degree}) = \frac{\text{Number of males without college degree}}{\text{Total number of people}} = \frac{35}{100} = 0.35 \][/tex]
Therefore, the probabilities are:
- Probability of selecting a female: 0.44
- Probability of selecting a male: 0.56
- Probability of selecting a person with a college degree: 0.5
- Probability of selecting a person without a college degree: 0.5
- Probability of selecting a female with a college degree: 0.29
- Probability of selecting a male with a college degree: 0.21
- Probability of selecting a female without a college degree: 0.15
- Probability of selecting a male without a college degree: 0.35
