Question

1. college degrees awarded the table below represents the college degrees awarded in a recent academic year by gender. choose a degree at random. find the probability that it is a. a bachelors degree b. a doctorate or a degree awarded to a woman c. a doctorate awarded to a woman d. not a masters degree

Explanation:

Step1: Calculate total number of degrees

Add all values:

$$\begin{align*} &\text{Total}=573079 + 211381+24341+775424+301264+21683\\ &=573079+775424+(211381 + 301264)+(24341+21683)\\ &=1348503+512645+46024\\ &=1907172 \end{align*}$$

Step2: Solve part a (Bachelor's degree)

Number of Bachelor's degrees \(=573079 + 775424=1348503\)
Probability \(P=\frac{\text{Number of Bachelor's degrees}}{\text{Total}}\)
\(P=\frac{1348503}{1907172}\approx0.707\)

Step3: Solve part b (Doctorate or degree awarded to a woman)

Number of Doctorates \(=24341+21683 = 46024\)
Number of degrees awarded to women \(=775424+301264+21683=1098371\)
Number of Doctorates awarded to women \(=21683\)
Using formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
\(P=\frac{46024 + 1098371-21683}{1907172}=\frac{1122712}{1907172}\approx0.589\)

Step4: Solve part c (Doctorate awarded to a woman)

Number of Doctorates awarded to women \(=21683\)
Probability \(P=\frac{21683}{1907172}\approx0.0114\)

Step5: Solve part d (Not a master's degree)

Number of master's degrees \(=211381+301264 = 512645\)
Number of non - master's degrees \(=1907172-512645 = 1394527\)
Probability \(P=\frac{1394527}{1907172}\approx0.731\)

Answer:

a. Approximately \(0.707\)
b. Approximately \(0.589\)
c. Approximately \(0.0114\)
d. Approximately \(0.731\)