Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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?
(a)
The probability of selecting a red marble and then replacing it is:
P(red) = number of red marbles / total number of marbles
P(red) = 4 / (4+7+5) = 4 / 16 = 1/4
Since the red marble is replaced, the total number of marbles is still 16 when selecting a blue marble:
P(blue) = number of blue marbles / total number of marbles
P(blue) = 7 / 16
The probability of both events happening is the product of their individual probabilities:
P(red and blue) = P(red) * P(blue)
P(red and blue) = (1/4) * (7/16) = 7/64
(b)
The probability of selecting a red marble and then setting it aside is the same as in part (a):
P(red) = 4 / 16 = 1/4
However, since the red marble is not replaced, there are now only 15 marbles in the jar when selecting a blue marble:
P(blue) = number of blue marbles / total number of marbles
P(blue) = 7 / 15
The probability of both events happening is the product of their individual probabilities:
P(red and blue) = P(red) * P(blue)
P(red and blue) = (1/4) * (7/15) = 7/60
(c)
The answers for parts (a) and (b) are not the same. The probabilities are different since the red marble is replaced in part (a) but not in part (b). This changes the total number of marbles and affects the probability of selecting a blue marble.