Question

Assuming a person from this survey is selected at random, what is the probability that a person perfers rap music given that the person is female?​

Answer 1

The probabiliy of selecting a person who prefeers rap if the person is female an be calculated as the proportion of women who prefeer rap music: 23.6%.

Explanation:

• The total amount of persons in the survey is 200: women in the sample equal to 106 ( 54 of them preferred techno music, 45 of them prefeer rap and 27 of them prefeer country music), while there are 94 men in the sample (36 of them preferred techno music, 40 of them prefeer rap and 18 of them prefeer country music).

• The probabiliy of selecting a person who prefeers rap if the person is female can be calculated as the proportion of women who prefeer rap music:
  `(25)/(106)=23.6\%`.
• Knowing that the person is a female gives you information, you are no longer looking at the 200 person survey, you are interest in a part of it: the women participants. Then, conditional on knowing that the person is a women (then, we are looking at the 106 cases in which the persons of the survey are women), we now find the probability of finding women who prefeer rap music: 25 between 106 cases, which is
  `23.6\%` .