Answer: The required probability is [tex]\dfrac{5}{18}.[/tex]
Step-by-step explanation: Given that a bag contains 5 red marbles and 4 green marbles.
We are to find the probability of choosing a red marble then a green marble, without replacement.
Total number of balls in the bag = 5 + 4 = 9.
The probability of choosing a red marble is given by
[tex]P_r=\dfrac{\textup{number of red balls}}{\textup{total number of balls}}=\dfrac{5}{9}.[/tex]
Since the second balls is chosen without replacing the first ball, so
the total number of balls remained in the bag = 4 + 4 = 8.
And the probability of choosing a green ball without replacement is
[tex]P_g=\dfrac{\textup{number of green balls}}{\textup{total number of balls remained in the bag}}=\dfrac{4}{8}=\dfrac{1}{2}.[/tex]
Therefore, the probability of choosing a red marble then a green marble, without replacement is given by
[tex]P=P_r\times P_g=\dfrac{5}{9}\times \dfrac{1}{2}=\dfrac{5}{18}.[/tex]
Thus, the required probability is [tex]\dfrac{5}{18}.[/tex]
