You are at the movies ith your friends and decided to buy a small bag of gummy bears. There are 4 red bears, 5 green bears, and 3 yellow bears in the bag. What is the probability that you will get yellow gummy bears and then red gummy bears?
First, we need to find the total number of gummy bears in the bag:
Total gummy bears = 4 (red) + 5 (green) + 3 (yellow) = 12 bears
The probability of selecting a yellow gummy bear first is:
P(yellow) = Number of yellow bears / Total number of bears = 3/12 = 1/4
After selecting a yellow gummy bear, there will be 2 yellow bears left in a total of 11 bears.
The probability of selecting a red gummy bear second is:
P(red after yellow) = Number of red bears / Total number of bears after selecting yellow = 4/11
To find the probability of both events happening (yellow gummy bears and then red gummy bears), we multiply the probabilities:
P(yellow and red) = P(yellow) * P(red after yellow)
P(yellow and red) = (1/4) * (4/11) = 1/11
So, the probability of selecting yellow gummy bears first and then red gummy bears is 1/11.