Dependent Probability

The Previous Action Affects the Next

A common example is when an event can be taken away. For example, you have a jar of 20 gumballs. There are 5 each of red, blue, green, and yellow. Starting off, you have a 1 in 4 chance of pulling any color because 5/20 = 1/4.

Twenty Gumballs with Even-Numbered Colors

Once one gumball has been chosen, the probability changes, thus the probability is dependent. Let’s say that on our first pull we removed 1 red gumball. There are still 5 gumballs each of blue, green and yellow in the bowl, but now only 4 red gumballs. The total gumballs in the bowl is 19. If we are hoping to pull another red gumball on the second pull, the probability is no longer 1/4. The new probability of pulling a red gumball is 4/19.

Removing One Gumball Changes the Probability