Question

You go to a dance and help clean up afterwards. To help, you collect the soda cans, Coca-Cola and Sprite, and organize them. Some cans were on the table and some were in the garbage. Seventy-two total cans were found. 42 total cans were found in the garbage and fifty total cans were Coca-Cola. 14 Sprite cans were found on the table. Draw and complete the two-way frequency chart, on a piece of paper, to help answer the question.

What is the probability that a randomly selected can was found on the table given that it was a Coca-Cola can?
P(table|Coca-Cola)=
Round your answer to the nearest hundredth.

Answer 1

Table | Garbage
------|--------
Coca-Cola | ? | ?
Sprite | 14 | ?

To fill in the missing values in the table, we can use the given information:

- 72 total cans were found, so the sum of all four cells in the table must be 72.
- 42 cans were found in the garbage, so the sum of the two cells in the "Garbage" column must be 42.
- 50 cans were Coca-Cola, so the sum of the two cells in the "Coca-Cola" row must be 50.
- 14 Sprite cans were found on the table, so the cell in the "Sprite" row and "Table" column must be 14.

Using this information, we can fill in the remaining cells:

Table | Garbage
------|--------
Coca-Cola | 36 | 14
Sprite | 14 | 8

To find the probability that a randomly selected can was found in the garbage, we add up the number of cans found in the garbage and divide by the total number of cans:

P(Garbage) = (42 + 8) / 72 = 0.625 or 62.5%

To find the probability that a randomly selected can was Coca-Cola, we add up the number of Coca-Cola cans and divide by the total number of cans:

P(Coca-Cola) = 50 / 72 = 0.694 or 69.4%


Does this help?