# PUZZLOR

### Deserted island

#### John Toczek

puzzlor@gmail.com

You find yourself washed up on a deserted island with no water, shelter or food. In order to survive you need to quickly secure a water source, build a shelter and find a reliable food source (in that order).

Each day you will tackle these tasks one at a time until they are completed. The probability of you completing a task is outlined in Figure 1. For example, if you attempt to secure a water source on a particular day, you have a 20 percent chance of completing that task on that day.

Each day that you have not completed the task, there is a corresponding risk of death (also shown in the table). Your daily overall probability of death is calculated by summing up the probabilities of tasks that are not completed. For example, if you have secured the water source and built your shelter, then your daily probability of death is 5 percent (because you have not yet secured the food source).

Figure 1: Probability of completing a task.

Once you have completed the three tasks, your survival rate becomes 100 percent.

Question:

What is the probability you will survive?

Send your answer to puzzlor@gmail.com by June 15. The winner, chosen randomly from correct answers, will receive a \$25 Amazon Gift Card. Past questions can be found at puzzlor.com.

John Toczek is the senior director of Decision Support and Analytics for Aramark Corporation in the Global Operational Excellence group. He earned his BSc. in chemical engineering at Drexel University (1996) and his MSc. in operations research from Virginia Commonwealth University (2005).