Final answer:
The probabilities for the student being female, dropping out, being both female and a dropout, a female student dropping out, and a dropout being female are calculated using the given data and basic probability rules.
Step-by-step explanation:
To solve the student's question, let’s first summarize the data provided. There are 317,000 high school students, with 154,000 identified as girls and 163,000 as boys. Out of the girls, 46,400 dropped out, and 10,100 boys dropped out.
- (a) The probability that the student is female is the number of girls divided by the total number of students: P(Female) = 154,000 / 317,000 = 0.4858 or 48.58%.
- (b) The probability that the student dropped out is the combined number of students who dropped out divided by the total number of students: P(Dropout) = (46,400 + 10,100) / 317,000 = 56,500 / 317,000 = 0.1782 or 17.82%.
- (c) The probability that the student is female and dropped out is the number of girls who dropped out divided by the total number of students: P(Female and Dropout) = 46,400 / 317,000 = 0.1464 or 14.64%.
- (d) Given that the student is female, the probability that she dropped out is the number of girls who dropped out divided by the total number of girls: P(Dropout | Female) = 46,400 / 154,000 = 0.3013 or 30.13%.
- (e) Given that a student dropped out, the probability that the student is female is the number of girls who dropped out divided by the total number of dropouts: P(Female | Dropout) = 46,400 / 56,500 = 0.8214 or 82.14%.