A bag contains 5 red balls, 6 blue balls, and 9 green balls. What is the probability of drawing a red ball followed by a blue ball without replacement?
To calculate the probability of two events happening in sequence, we multiply the probabilities of each event occurring independently. In this case, we want to find the probability of drawing a red ball first and then a blue ball without replacing the red ball back into the bag.

First, let's find the probability of drawing a red ball:
There are 5 red balls and a total of 20 balls in the bag (5 + 6 + 9).
Probability of drawing a red ball = Number of red balls / Total number of balls
                                                   = 5/20
                                                   = 1/4

Next, since we're not replacing the red ball, there will be 19 balls left in the bag, with 6 of them being blue.
Probability of drawing a blue ball after drawing a red ball = Number of blue balls / Total number of remaining balls
                                                                                          = 6/19

Now, we multiply the probabilities together:
Probability of drawing a red ball followed by a blue ball = (1/4) * (6/19)
                                                                                        = 6/76

So, the probability of drawing a red ball followed by a blue ball without replacement is 6/76.