Final answer:
The probability of one person randomly picking a cherry popsicle then another person selecting a grape popsicle from the box is 1/15.
Step-by-step explanation:
To find the probability of one person randomly picking a cherry popsicle and then another person selecting a grape popsicle from the box, we need to first determine the total number of popsicles and the number of cherry and grape popsicles.
There are a total of 4 flavors and 4 popsicles of each flavor in the box, so there are 4 x 4 = 16 popsicles in total.
The probability of the first person picking a cherry popsicle is 4/16, since there are 4 cherry popsicles in the box.
After the first person has picked a cherry popsicle, there are now 3 cherry popsicles remaining in the box and 15 popsicles in total.
The probability of the second person selecting a grape popsicle is 4/15, since there are 4 grape popsicles remaining in the box.
To find the overall probability, we multiply the probability of the first person picking a cherry popsicle by the probability of the second person selecting a grape popsicle:
Probability = (4/16) x (4/15) = 16/240 = 1/15.