probability question

Question

In a recent school year in the state of Washington, there were 

320,000 high school students. Of these, 156,000 were female and 164,000 were male. Among the females, 11,400 dropped out of school, and among the males, 10,300 dropped out. A student is chosen at random. Round the answers to four decimal places.(a) What is the probability that the student is male?

(b) What is the probability that the student dropped out?

(c) What is the probability that the student is male and dropped out?

(d) Given that the student is male, what is the probability that he dropped out?

(e) Given that the student dropped out, what is the probability that the student is male?

Answer 1

21,700 students dropped out out of 320,000 students total. Thus, 21,700/320,000 = 0.0678 is the probability that a student dropped out.

b) 10,300 students who were male dropped out. Out of the total, this is 10,300/320,000 = 0.0322 is the probability that a student is male and dropped out.

c) Of the male students only, 10,300 dropped out. This means that 10,300/164,000 = 0.0628 is the probability that, given a male student, they will drop out.

d) 21,700 students dropped out overall and 10,300 who dropped out were male. Dividing these quantities gives 10,300/21,700 = 0.475 which is the probability that a student who dropped out is male.