Answer: The required probability is [tex]\dfrac{2}{15}.[/tex]
Step-by-step explanation: Given that an urn contains 6 red marbles and 4 black marbles. Two marbles are randomly drawn one by one from the urn without replacement.
We are to find the probability that both drawn marbles are black.
Let E and F denote the events of two marbles one by one without replacement and let S and S' denote the corresponding sample spaces.
Then, we have
[tex]n(E)=^4C_1=4,\\\\n(F)=^3C_1=3,\\\\n(S)=^{10}C_1=10,\\\\n(S')=^9C_1=9.[/tex]
Therefore, the probability that both marbles are red is given by
[tex]p=P(E)\times P(F)=\dfrac{n(E)}{n(S)}\times\dfrac{n(F)}{n(S')}=\dfrac{4}{10}\times\dfrac{3}{9}=\dfrac{2}{15}.[/tex]
Thus, the required probability is [tex]\dfrac{2}{15}.[/tex]
