Probability with “not”

Probability questions with not are similar to normal probability questions. The main difference is that the odds that need to be calculated are the odds of failure rather than success.

In the earlier examples on probability, the focus was on drawing a specific color of starburst out of a bag. The odds there were simply: 

# of starbursts of that color# starbursts in total

If the question were changed to “what are the odds of drawing a color that is not red out of a bag of starbursts”, then the odds are simply equal to: 

# non–red starbursts# total starbursts in the bag. So instead of adding up the red starbursts, add up all of the other colors.

Another way to think about it is that the probability of something not happening is equal to: 1 − P_s where P_sis defined as the odds of that same thing happening. Since probability is just a likelihood out of 1 (or 100%), the odds of success and failure always add up to 1. So a student can also simply calculate the odds of success, and then subtract that from 1.