Question

The table to the right shows the number of men and​ women, in​ thousands, enrolled in​ degree-granting institutions in a certain year. The men and women are categorized by their age groups. Complete parts​ a) through​ f) below.

Men Women 14 to 17 years old 1313 1010 18 and 19 years old 274274 322322 20 and 21 years old 281281 452452 22 to 24 years old 542542 681681 25 to 29 years old 433433 829829 30 to 34 years old 430430 448448 35 years old and older 793793 1 comma 4441,444

​a) Determine the probability of selecting a female.

​(Round to three decimal places as​ needed.)

​b) Determine the probability of selecting a student that is 22 to 24 years old.

​(Round to three decimal places as​ needed.)

​c) Determine the probability of selecting a woman who is 35 years old or older.

​(Round to three decimal places as​ needed.)

​d) Determine the probability of selecting either a student who is a woman or is 25 to 29 years old.

​(Round to three decimal places as​ needed.)

​e) Determine the probability of selecting a​ man, given that the student is 22 to 24 years old.

​(Round to three decimal places as​ needed.)

​f) Determine the probability of selecting a student that is 30 to 34 years​ old, given that the student is a man.

Answer 1

Solution:-

	Men	Women
14 to 17 years old	13	10
18 to 19 years old	274	322
20 to 21 years old	281	452
22 to 24 years old	542	681
25 to 29 years old	433	829
30 to 34 years old	430	448
35 years old and older	793	1444
Total	2766	4186

​a) The probability of selecting a female is 0.602.

Total number of people = 4186 + 2766 = 6952

Number of females enrolled = 4186

The probability of selecting a female = 4186/6952

The probability of selecting a female is 0.602

​b) The probability of selecting a student that is 22 to 24 years old is 0.176

Total number of people = 4186 + 2766 = 6952

Number of students that is 22 to 24 years old = 1223

The probability of selecting a student that is 22 to 24 years old = 1223/6952

The probability of selecting a student that is 22 to 24 years old is ​0.176

c) The probability of selecting a woman who is 35 years old or older is 0.208

Total number of people = 4186 + 2766 = 6952

Number of females who are 35 years old or older = 1444

The probability of selecting a woman who is 35 years old or older = 1444/6952

The probability of selecting a woman who is 35 years old or older is 0.208

​d) The probability of selecting either a student who is a woman or is 25 to 29 years old is 0.664.

Total number of people = 4186 + 2766 = 6952

Number of students who are woman or is 25 to 29 years old = 4186 + 433 = 4619

The probability of selecting either a student who is a woman or is 25 to 29 years old = 4619/6952

The probability of selecting either a student who is a woman or is 25 to 29 years old is 0.664.