Problem of the Week - Middle School - Nov. 29, 2020 to Dec. 5, 2020

Middle School: 

Question: Jenny is making a number of treat bags for her birthday party guests. She buys a bag of 50 lollipops, 8 of which are blue raspberry-flavored. Before distributing the lollipops amongst the treat bags, Jenny randomly picks 3 lollipops to keep for herself. Whatever she picks, she keeps. What is the probability that all 3 lollipops Jenny picks are blue raspberry-flavored? Round your answer to the nearest hundredth of a percent. 

Answer: 0.29%

Solution:  The probability that the first lollipop Jenny picks will be blue raspberry-flavored is 8 lollipops out of 50 total lollipops = 8/50 = 4/25. If she picks this flavor, then the probability of the second lollipop being the same flavor is 8 – 1/50 – 1 = 7/49 = 1/7. If she picks this flavor for the first and the second, then the probability of the third lollipop being the same flavor is 7 – 1/49 – 1 = 6/48 = 1/8. The probability of all of these events occurring is 4/25 × 1/7 × 1/8 = 4/1,400 ≈ 0.29%.