The table shows the educational attainment of the population of Mars, ages 25 and over, expressed in millions. Find the probability that a randomly selected martian, aged 25 and over has completed four years of high school only or is a male. The probability is 107 157 Male Female Total Years of High School Less than 4 4 only 24 33 57 (Type an integer or a simplified fraction.) 12 15 27 C Years of College Some (less than 4) 20 19 39 4 or more 18 16 34 Total 74 83 157

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The table shows the educational attainment of the population of Mars, ages 25 and over, expressed in millions. It provides the data required to find the probability that a randomly selected Martian, aged 25 and over, has completed four years of high school only or is a male.

### Table: Educational Attainment

|                | Years of High School |            | Years of College |            |        |
|----------------|----------------------|------------|------------------|------------|--------|
|                | Less than 4          | 4 only     | Some (less than 4) | 4 or more | Total  |
| Male           | 12                   | 24         | 20               | 18         | 74     |
| Female         | 15                   | 33         | 19               | 16         | 83     |
| Total          | 27                   | 57         | 39               | 34         | 157    |

### Analysis

1. **Columns and Rows:**
   - Columns represent years of education completed.
   - Rows represent the population divided by gender.
  
2. **Data Interpretation:**
   - Total number of males is 74.
   - Total number of females is 83.
   - Total population is 157.

3. **Probability Calculation:**
   - We need to find the probability that a randomly selected individual is either a male or has completed four years of high school only.
   - The total number of individuals with four years of high school only is 57 (sum of 24 males and 33 females).
   - The number of males is already included in the total, which is 74.
   - Add the two, then subtract overlap (males who completed only four years of high school, already counted in both), so we have 74 + 57 - 24 = 107.
   - Total individuals is 157.

Therefore, the probability is \( \frac{107}{157} \).
Transcribed Image Text:The table shows the educational attainment of the population of Mars, ages 25 and over, expressed in millions. It provides the data required to find the probability that a randomly selected Martian, aged 25 and over, has completed four years of high school only or is a male. ### Table: Educational Attainment | | Years of High School | | Years of College | | | |----------------|----------------------|------------|------------------|------------|--------| | | Less than 4 | 4 only | Some (less than 4) | 4 or more | Total | | Male | 12 | 24 | 20 | 18 | 74 | | Female | 15 | 33 | 19 | 16 | 83 | | Total | 27 | 57 | 39 | 34 | 157 | ### Analysis 1. **Columns and Rows:** - Columns represent years of education completed. - Rows represent the population divided by gender. 2. **Data Interpretation:** - Total number of males is 74. - Total number of females is 83. - Total population is 157. 3. **Probability Calculation:** - We need to find the probability that a randomly selected individual is either a male or has completed four years of high school only. - The total number of individuals with four years of high school only is 57 (sum of 24 males and 33 females). - The number of males is already included in the total, which is 74. - Add the two, then subtract overlap (males who completed only four years of high school, already counted in both), so we have 74 + 57 - 24 = 107. - Total individuals is 157. Therefore, the probability is \( \frac{107}{157} \).
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