Given:
Sarah has 1 red cube, 1 green cube, 1 purple cube, and 1 black cube.
Sarah picks two items from the bag without replacement.
We need to determine the probability that she will pick a red cube and then a black cube.
Probability:
The probability to pick a red cube is [tex]P(R)=\frac{1}{4}[/tex]
The probability to pick a black cube without replacement is [tex]P(B)=\frac{1}{3}[/tex]
The probability to pick a red cube and then a black cube is given by
[tex]P(RB)=P(R) \cdot P(B)[/tex]
Substituting the values, we have;
[tex]P(RB)=\frac{1}{4} \cdot \frac{1}{3}[/tex]
[tex]P(RB)=\frac{1}{12}[/tex]
Thus, the probability that Sarah will pick a red cube and then a black cube is [tex]\frac{1}{12}[/tex]
