23. A box contains four different computer disks, labeled 1, 2, 3, and 4. Two disks are selected at random from the box “with replacement,” meaning that after the first selection is made, the selected disk is returned to the box before the second selection is made. “At random”

means that all disks in the box have an equal chance of being selected.

a. Define the sample space for this experiment.

b. Is the event of choosing disk 1 or 3 on the first selection independent of choosing disk 1 or 2 on the second selection? Why or why not?

c. Is the event of choosing disk 1 on the first selection independent of choosing disk 1 on the second selection? Why or why not?

d. Is the event of choosing disk 1 on both the first and second selections independent of the event that neither disk 3 nor 4 is chosen in the selection process?