Probability questions?

there are 1300 people surveyed on job satisfaction: 750 men %26amp; 550 women


Suppose that one of the 1300 employees surveyed is chosen at random:





1. What is the probability that he or she feels that a good relationship with the boss is extremely important?





2. What is the probability that the employee is a female who feels that a good relationship with the boss is extremely important?





3. Given that the chosen employee considers that having a good relationship with the boss is extremely important, what is the probability that this employee is a female?





Here is the data needed:


Good Relationship with Boss: Men:61% Women: 77%





thank you very much

Probability questions?
M = Male


F = Female


G = Good relationship with boss.


P(M) = 750/1300 (probability that the chosen person is male)


P(F) = 550/1300 (probability that the chosen person is female)


P(G/M)=0.61


P(G/F)=0.77


1) P(G) = P(M) P(G/M)+ P(F) P(G/F)


P(G) = (750/1300) (0.61) + (550/1300)(0.77)


0.3519+0.3258=0.6777





2)P(F)P(G/F)= (550/1300)(0.77)=0.3258





3)P(F/G) = P(F)P(G/F) / [P(F)P(G/F)+P(M)P(G/M)]


= (550/1300)(0.77) / 0.6777


You can simplify this.
Reply:1. You must add the number of satisfied men and women and divide by the total number of applicants, and then multiply by 100%.





61% MALE of 750 = 457.5


77% FEMALE of 550 = 423.5


457.5 + 423.5 = 881


(881/ 1300) x 100% =


ANSWER 67.6%





2. There are 423.5 females who feel a good relationship with the boss is important. You take this number and divide by the total number of applicants, and then multiply by 100% to get your answer.


(423.5 / 1300) x 100% = 32.57%





3. You must divide the number of females who think a relationship with the boss is important (423.5) by the total number of people who feel that way (881), and then multiply by 100%.


(423.5 / 881) x 100% = 48.07%