In: Statistics and Probability
[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.]
a. What is the probability of selecting a red marble, replacing it,
and then selecting a blue marble? Show your work.
b. What is the probability of selecting a red marble, setting it
aside, and then selecting a blue marble? Show your work.
c. Are the answers to parts (a) and (b) the same? Why or why
not?
Total number of marbles = 4 + 7 + 5 = 16
a) P(selecting a red marble, replacing it, and then selecting a blue marble) = 4/16 x 7/16
= 7/64
b) P(selecting a red marble, setting it aside, and then selecting a blue) = 4/16 x 7/15
= 7/60
c) The answers are not the same. In part (b), when the second marble is taken, the number of marbles from which we take the second one is 15. This is because we did not replace the first marble. So, the probability changes.