Probability question dealing with an or statement.

Question

A bag contains 9 Buttercups & 3 Kisses. A box contains 4 Jolly Ranchers, 6 Life Savers, and 10 Werthers. If we randomly select 1 item out of the bag & 1 item from the box what is the probability one will select: 

a) a Buttercup or Werther?

 

Our question is can you solve this problem by doing it this way because or means we need to add the probabilities together.  Problem is the result is greater than 1 and in probability 1 means it certain to happen so no result should be greater than 1.

 

9/12 + 10/20 = 180/240 + 120/240 = 300/240 = 5/4

 

or

 

would it have to be solved this way since you are only looking at picking one item out of the total amount of candies in the end which is either 1 buttercup or 1 werthers. 

 

9/32 + 10/32 = 19/32

Answer 1

I think the wording is misleading. You have two different experiments; picking from a bag and picking from a box.

Maybe the wording should be "What is the probability of picking a Buttercup from the bag or picking a Werther from the box ?" The probability of picking the Buttercup from the bag is 9/12 or 3/4. The probability of picking a Werther from the bag is 10/20 or 1/2. Just because it says "or" doesn't mean you add these probabilities. So your answer should be 3/4 or 1/2.