Question

Sarah has 1 red cube, 1 green cube, 1 purple cube, and 1 black cube. If Sarah picks two items from the bag, without replacing, what is the probability she will pick a red cube and then a black cube?

Answer 1

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
`P(R)=(1)/(4)`

The probability to pick a black cube without replacement is
`P(B)=(1)/(3)`

The probability to pick a red cube and then a black cube is given by

`P(RB)=P(R) \cdot P(B)`

Substituting the values, we have;

`P(RB)=(1)/(4) \cdot (1)/(3)`

`P(RB)=(1)/(12)`

Thus, the probability that Sarah will pick a red cube and then a black cube is
`(1)/(12)`