Problem of the Week
Problem A
Halloween Candy

After going trick-or-treating on Halloween, James, Robbie, and Ginny come home with the following treats:

• James: \(6\) chocolate bars, \(4\) caramels, \(6\) suckers, \(5\) licorice

• Robbie: \(5\) chocolate bars, \(5\) caramels, \(3\) suckers, \(7\) licorice

• Ginny: \(2\) chocolate bars, \(8\) caramels, \(4\) suckers, \(6\) licorice

They decide to put all of their treats into a single bucket. Each day, James, Robbie, and Ginny each randomly pick \(2\) treats from the bucket to enjoy.

1. Assuming that each individual treat is equally likely to be selected, on the first day, which type of treat is most likely to be picked from the bucket?

2. Assuming that each individual treat is equally likely to be selected, on the first day, which types of treats are equally likely to be picked from the bucket?

3. How many days must Robbie pick treats from the bucket to guarantee that he picks the same type of treat more than once?

4. How many days must James, Robbie, and Ginny each pick from the bucket to guarantee that at least one of them has picked a piece of licorice at least once?

Theme: Data Management