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.
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?