Question

The Following table lists the probabilities of unemployed females and males and their educational attainment.

                                                                   Female Male

Less than High School    .077    .110

High School Graduate    .154                               .201

Some College/University-no degree .141 .129

College/University Graduate                            .092 .096

a) If one unemployed person is selected at random, what is the probability that he or she did not finish high school? Carry answer to the nearest thousandths

b) If an unemployed female is selected at random, what is the probability that she has a college or university degree? Carry answer to the nearest ten-thousandths

c) If an unemployed high school graduate is selected at random, what is the probability that he is a male? Carry answer to the nearest ten-thousandths

Answer 1

a) If one unemployed person is selected at random the probability that he or she did not finish high school:

Since we are given the the probabilities of unemployed females and males, if one unemployed person is selected at random (Male or female), we should find the probability that the selected person did not finish high school.

Let L be the event that if one unemployed person is selected at random, and he or she did not finish high school.

Let L_M be the event that the randomly selected unemployed person is male and he didnt finish high school. That is P[L_M] = 0.110

Let L_F be the event that the randomly selected unemployed person is female and she didnt finish high school. That is P[L_F] = 0.077

The probability that randomly selected unemployed person did not finish high school = Probability that selected unemployed person is male and he didnt finish high school + Probability that selected unemployed person is female and she didnt finish high school.

Thus if one unemployed person is selected at random, the probability that he or she did not finish high school is 0.187 or 18.7%

​​(b) If an unemployed female is selected at random, the probability that she has a college or university degree:

Let F be the event that randomly selected unemployed person is female. Let F_L be the event​ that randomly selected unemployed person is female and less than high school. Let F_H be the event​ that randomly selected unemployed person is female and high school graduate. Let F_S​ be the event​ that randomly selected unemployed person is female and some college/university-no degree. Let F_C​ be the event​ that randomly selected unemployed person is female and College/University graduate.

Thus the probability that the randomly selected unemployed person is female = probability that person is female and less than high school + probability that person is female and high school graduate + probability that person is female and some college/university-no degree + probability that person is female and College/University graduate.

  

Now let R be the event that randomly selected unemployed person has a college or university degree. And ​ be the event that randomly selected unemployed person is female and has college/university degree. Thus

Now if an unemployed female is selected at random, the probability that she has a college or university degree is given by ​ (That is the probability that randomly selected unemployed person has college/university degree given that the female unemployed person is already selected)

Thus if an unemployed female is selected at random, the probability that she has a college or university degree is 0.1983 or 19.83%.

(c) If an unemployed high school graduate is selected at random, the probability that he is a male:

Let H be the event that randomly selected person is unemployed high school graduate. Let H_M be the event that randomly selected person is unemployed high school graduate and male. Let H_F be the event that randomly selected person is unemployed high school graduate and female.

Thus probability that the randomly selected person is unemployed high school graduate = probability that the randomly selected person is unemployed high school graduate​ and male + probability that the randomly selected person is unemployed high school graduate and female.

Let M be the event that randomly selected unemployed person is Male. Let ​ be the event that randomly selected unemployed person is Male and High school graduate. Thus

Now if an unemployed high school graduate is selected at random, the probability that he is a male is given by ​ (That is the probability that randomly selected person is male given that unemployed high school graduate is randomly selected already).

  

  

  

Thus if an unemployed high school graduate is selected at random, the probability that he is a male is 0.566 or 56.6%.