The diagram below shows the contents of a jar from which you select marbles at random.
An illustration of a jar of marbles is shown. Four of the marbles are labeled with an upper R, seven of the marbles are labeled with an upper B, and five of the marbles are labeled with an upper G. The key identifies upper R to represent red marbles, upper B to represent blue marbles, and upper G to represent green marbles.
What is the probability of selecting a red marble, replacing it, and then selecting a blue marble? Show your work.
What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? Show your work.
Are the answers to parts (a) and (b) the same? Why or why not?
a) The probability of selecting a red marble and replacing it is given by $\frac{4}{16} = \frac{1}{4}$. After replacing the red marble, there are still 16 marbles in the jar, so the probability of selecting a blue marble is $\frac{7}{16}$. Thus, the probability of both events happening is $(\frac{1}{4})\times(\frac{7}{16}) = \frac{7}{64}$.
b) The probability of selecting a red marble and setting it aside is given by $\frac{4}{16} = \frac{1}{4}$. After setting the red marble aside, there are only 15 marbles left in the jar, so the probability of selecting a blue marble is $\frac{7}{15}$. Thus, the probability of both events happening is $(\frac{1}{4})\times(\frac{7}{15}) = \frac{7}{60}$.
c) No, the answers to parts (a) and (b) are not the same because in part (a), the red marble is replaced, which means that the number of marbles in the jar remains the same for the second draw, but in part (b), the red marble is set aside, which means that the number of marbles in the jar decreases for the second draw. This changes the probability of selecting a blue marble in the second draw.