Questions: MAT 143 Statistics Activity 5 - Chapter 3 (Probability) The table shows the numbers (in thousands) of earned degrees by level in two different fields, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics) Level of Degree Natural sciences/mathematics Computer science/engineering Total ------------------------------------------------------------------------------------ Bachelor's 175.5 220.3 395.8 Master's 34.8 105.4 140.2 Doctoral 16.4 13.0 29.4 TOTAL 226.7 338.7 565.4 PLEASE SHOW THE FRACTIONS YOU USE TO CALCULATE YOUR ANSWERS. 1. A person who earned a degree in this year is randomly selected. Find the probability (rounded to the nearest thousandth) that the degree earned by the person is a: A. Bachelor's degree B. Bachelor's degree, given that the degree is in computer science/engineering C. Bachelor's degree, given that the degree is not in computer science/engineering D. Bachelor's degree or master's degree E. Doctorate, given that the degree is in computer science/engineering F. Master's degree or the degree is in natural sciences/mathematics G. Bachelor's degree and the degree is in natural sciences/mathematics H. Degree in computer science/engineering, given that the person earned a bachelor's degree I. Master's degree and doctorate degree J. Degree in computer science/engineering or degree in natural sciences/mathematics 2. Which of the event(s) in parts A through J can be considered unusual? Explain. 3. Which of the event(s) in parts A through J can be considered mutually exclusive? Explain.

MAT 143 Statistics Activity 5 - Chapter 3 (Probability) The table shows the numbers (in thousands) of earned degrees by level in two different fields, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics) Level of Degree Natural sciences/mathematics Computer science/engineering Total ------------------------------------------------------------------------------------ Bachelor's 175.5 220.3 395.8 Master's 34.8 105.4 140.2 Doctoral 16.4 13.0 29.4 TOTAL 226.7 338.7 565.4 PLEASE SHOW THE FRACTIONS YOU USE TO CALCULATE YOUR ANSWERS. 1. A person who earned a degree in this year is randomly selected. Find the probability (rounded to the nearest thousandth) that the degree earned by the person is a: A. Bachelor's degree B. Bachelor's degree, given that the degree is in computer science/engineering C. Bachelor's degree, given that the degree is not in computer science/engineering D. Bachelor's degree or master's degree E. Doctorate, given that the degree is in computer science/engineering F. Master's degree or the degree is in natural sciences/mathematics G. Bachelor's degree and the degree is in natural sciences/mathematics H. Degree in computer science/engineering, given that the person earned a bachelor's degree I. Master's degree and doctorate degree J. Degree in computer science/engineering or degree in natural sciences/mathematics 2. Which of the event(s) in parts A through J can be considered unusual? Explain. 3. Which of the event(s) in parts A through J can be considered mutually exclusive? Explain.
Transcript text: MAT 143 Statistics Activity 5 - Chapter 3 (Probability) The table shows the numbers (in thousands) of earned degrees by level in two different fields, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics) \begin{tabular}{|l|l|l|l|l|} \cline { 4 - 5 } \multicolumn{2}{|c|}{} & \multicolumn{3}{c|}{ Field } \\ \cline { 3 - 5 } \multicolumn{2}{c|}{} & \begin{tabular}{l} Natural \\ sciences/mathematics \end{tabular} & \begin{tabular}{l} Computer \\ science/engineering \end{tabular} & Total \\ \hline \multirow{3}{*}{\begin{tabular}{l} Level of \\ Degree \end{tabular}} & Bachelor's & 175.5 & 220.3 & 395.8 \\ \cline { 2 - 5 } & Master's & 34.8 & 105.4 & 140.2 \\ \cline { 2 - 5 } & Doctoral & 16.4 & 13.0 & 29.4 \\ \hline & TOTAL & 226.7 & 338.7 & 565.4 \\ \hline \end{tabular} LEASE SHOW THE FRACTIONS YOU USE TO CALCULATE YOUR ANSWERS. 1. A person who earned a degree in this year is randomly selected. Find the probability (rounded to the nearest thousandth) that the degree earned by the person is a: A. Bachelor's degree B. Bachelor's degree, given that the degree is in computer science/engineering C. Bachelor's degree, given that the degree is not in computer science/engineering D. Bachelor's degree or master's degree E. Doctorate, given that the degree is in computer science/engineering F. Master's degree or the degree is in natural sciences/mathematics G. Bachelor's degree and the degree is in natural sciences/mathematics H. Degree in computer science/engineering, given that the person earned a bachelor's degree I. Master's degree and doctorate degree J. Degree in computer science/engineering or degree in natural sciences/mathematics 2. Which of the event(s) in parts A through J can be considered unusual? Explain. 3. Which of the event(s) in parts A through J can be considered mutually exclusive? Explain.
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Solution

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Solution Steps

To solve the given probability questions, we will use the provided data to calculate the required probabilities. The total number of degrees conferred is 565.4 thousand. We will use this total to find the probabilities for each specific event.

  1. Probability Calculations:
    • A. Probability of a Bachelor's degree.
    • B. Probability of a Bachelor's degree given that the degree is in computer science/engineering.
    • C. Probability of a Bachelor's degree given that the degree is not in computer science/engineering.
    • D. Probability of a Bachelor's degree or a Master's degree.
    • E. Probability of a Doctorate given that the degree is in computer science/engineering.
    • F. Probability of a Master's degree or the degree is in natural sciences/mathematics.
    • G. Probability of a Bachelor's degree and the degree is in natural sciences/mathematics.
    • H. Probability of a degree in computer science/engineering given that the person earned a Bachelor's degree.
    • I. Probability of a Master's degree and a Doctorate degree.
    • J. Probability of a degree in computer science/engineering or a degree in natural sciences/mathematics.
Solution Approach
  1. Calculate the total number of degrees.
  2. Use the total to find the probability for each specific event.
  3. For conditional probabilities, use the relevant subset of the total.
Step 1: Total Degrees

The total number of degrees conferred is given by: \[ \text{Total Degrees} = 565.4 \text{ thousand} \]

Step 2: Probability of a Bachelor's Degree

The probability of a Bachelor's degree is calculated as: \[ P(\text{Bachelor's}) = \frac{395.8}{565.4} \approx 0.700 \]

Step 3: Probability of a Bachelor's Degree Given Computer Science/Engineering

The probability of earning a Bachelor's degree given that the degree is in Computer Science/Engineering is: \[ P(\text{Bachelor's} \mid \text{CS/Eng}) = \frac{220.3}{220.3 + 105.4 + 13.0} \approx 0.650 \]

Step 4: Probability of a Bachelor's Degree Given Not in Computer Science/Engineering

The probability of earning a Bachelor's degree given that the degree is not in Computer Science/Engineering is: \[ P(\text{Bachelor's} \mid \text{Not CS/Eng}) = \frac{175.5}{226.7} \approx 0.774 \]

Step 5: Probability of a Bachelor's or Master's Degree

The probability of earning either a Bachelor's or a Master's degree is: \[ P(\text{Bachelor's or Master's}) = \frac{395.8 + 140.2}{565.4} \approx 0.948 \]

Step 6: Probability of a Doctorate Given Computer Science/Engineering

The probability of earning a Doctorate given that the degree is in Computer Science/Engineering is: \[ P(\text{Doctorate} \mid \text{CS/Eng}) = \frac{13.0}{220.3 + 105.4 + 13.0} \approx 0.038 \]

Step 7: Probability of a Master's Degree or Degree in Natural Sciences/Mathematics

The probability of earning a Master's degree or a degree in Natural Sciences/Mathematics is: \[ P(\text{Master's or NS/Math}) = \frac{140.2 + 175.5 + 34.8 + 16.4}{565.4} \approx 0.649 \]

Step 8: Probability of a Bachelor's Degree and Degree in Natural Sciences/Mathematics

The probability of earning a Bachelor's degree and the degree being in Natural Sciences/Mathematics is: \[ P(\text{Bachelor's and NS/Math}) = \frac{175.5}{565.4} \approx 0.310 \]

Step 9: Probability of a Degree in Computer Science/Engineering Given Bachelor's Degree

The probability of earning a degree in Computer Science/Engineering given that the person earned a Bachelor's degree is: \[ P(\text{CS/Eng} \mid \text{Bachelor's}) = \frac{220.3}{395.8} \approx 0.557 \]

Step 10: Probability of a Master's Degree and Doctorate Degree

The probability of earning both a Master's degree and a Doctorate degree is: \[ P(\text{Master's and Doctorate}) = 0 \]

Step 11: Probability of a Degree in Computer Science/Engineering or Degree in Natural Sciences/Mathematics

The probability of earning a degree in Computer Science/Engineering or a degree in Natural Sciences/Mathematics is: \[ P(\text{CS/Eng or NS/Math}) = \frac{220.3 + 105.4 + 13.0 + 175.5 + 34.8 + 16.4}{565.4} = 1.000 \]

Final Answer

  • A. \( P(\text{Bachelor's}) \approx 0.700 \)
  • B. \( P(\text{Bachelor's} \mid \text{CS/Eng}) \approx 0.650 \)
  • C. \( P(\text{Bachelor's} \mid \text{Not CS/Eng}) \approx 0.774 \)
  • D. \( P(\text{Bachelor's or Master's}) \approx 0.948 \)
  • E. \( P(\text{Doctorate} \mid \text{CS/Eng}) \approx 0.038 \)
  • F. \( P(\text{Master's or NS/Math}) \approx 0.649 \)
  • G. \( P(\text{Bachelor's and NS/Math}) \approx 0.310 \)
  • H. \( P(\text{CS/Eng} \mid \text{Bachelor's}) \approx 0.557 \)
  • I. \( P(\text{Master's and Doctorate}) = 0 \)
  • J. \( P(\text{CS/Eng or NS/Math}) = 1.000 \)

Thus, the final boxed answers are: \[ \boxed{A \approx 0.700, B \approx 0.650, C \approx 0.774} \]

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