Question

A vending machine randomly dispenses gumballs of three flavors: orange, grape, and cherry. If the machine currently contains 20 orange, 12 grape, and 7 cherry gumballs, what is the least number of gumballs the machine must dispense in order to ensure that three orange gumballs have been dispensed

Answer 1

To ensure that three orange gumballs have been dispensed, we need to consider the worst-case scenario. The machine currently has 20 orange gumballs, and each time we dispense a gumball, there is a chance of getting an orange one. Therefore, to guarantee three orange gumballs, we should assume that the machine will dispense all the other flavors before dispensing three orange ones.

Step-by-step explanation:

To ensure that three orange gumballs have been dispensed, we need to consider the worst-case scenario. The machine currently has 20 orange gumballs, and each time we dispense a gumball, there is a chance of getting an orange one. Therefore, to guarantee three orange gumballs, we should assume that the machine will dispense all the other flavors before dispensing three orange ones.

So, there are a total of 20 + 12 + 7 = 39 gumballs that are not orange. To guarantee three orange gumballs, we need to dispense all of these non-orange gumballs plus three more orange ones, for a total of 39 + 3 = 42 gumballs.

Therefore, the least number of gumballs the machine must dispense to ensure three orange gumballs is 42.

Answer 2

22

Step-by-step explanation:

Find the worst case scenario.

Worst case:

12 grape gumballs, 7 cherry gumballs, and 3 orange gumballs.

12 + 7 + 3 = 22

The answer is 22 gumballs.

Hope this helps :)

Have a great day!