Exam 5: Randomness and Probability

A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time.Further, 15% of all steroid-free individuals also test positive.10% of the rugby team members use steroids.Your friend on the rugby team has just tested positive.The probability that he uses steroids is ________________________ .

During a promotion, Christina's department store offers a mailing "scratch a winner - discount savings." After customers select the items they wish to purchase, they scratch their discount sticker from the mailing to determine the discount they will receive.The scratch wheel is divided into 12 slices.Six slices are red and award a 10% discount, three slices are white and award a 20% discount, and two slices are blue and award a 40% discount.The remaining slice is gold and awards a 100% discount if the customer scratches that slice! The probability that a customer gets at least a 40% discount is ________________________ .