Given:
Given that there are 10 marbles in a bag. 4 are blue, 3 are black, 2 are white and 1 is red.
The marbles are selected by not replacing the drawn ones.
We need to the probability of selected a black marble and then a white marble without replacement.
Probability:
Let B denote the black marble.
Let W denote the white marble.
The probability of selecting a black marble is [tex]P(B)=\frac{3}{10}[/tex]
The probability of selecting a white marble without replacement is [tex]P(W)=\frac{2}{9}[/tex]
The probability of selecting a black marble and then a white marble without replacement is given by
[tex]P(B \ and \ W)=P(B) \cdot P(W)[/tex]
Substituting the values, we get;
[tex]P(B \ and \ W)=\frac{3}{10} \cdot \frac{2}{9}[/tex]
[tex]P(B \ and \ W)=\frac{6}{90}[/tex]
[tex]P(B \ and \ W)=\frac{1}{15}[/tex]
Thus, the probability of selecting a black marble and then a white marble without replacement is [tex]\frac{1}{15}[/tex]
