Probability word problems

Question

A school survey reported that 80% of students have cell phones, 45% have part time jobs, and 30% have both a cell phone and a part time job. If a student is chosen at random, what is the probability that the student has a part time job, given that they have a cell phone?

A. 25%

B. 32.5%

C. 35%

D. 37.5%

Answer 1

P(PTJ|CP)P(CP) = P(PTJ ∩ CP) One of Bayes Postulates (also = P(CP|PTJ)P(PTJ))

P(PTJ|CP) = P(PTJ ∩ CP)/P(CP) = 0.30/0.45) = 0.67 Not a given answer, so the wording may not mean what I think.

Form the Venn Diagram (pick a 100 students) If they have a cell phone ( 45 of original sample), they will have a part-time job (30 of original sample), so they are now 2/3 likely to have a PTJ. 50 people with PTJ were eliminated and 5 with neither are eliminated (45 left).