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Think of an event involving two coins that has probability of 75 %.
What is the theoretical probability of all 5 people being non-believers?
See solution.
See solution.
We are told that 75 % of people do not believe in ghosts. This tells us that 100-75 =25 % of people do believe in ghosts.
Ghost Non-Believers: & 75 % Ghost Believers: & 25 % We want to design a simulation that would estimate the probability of randomly selecting 5 non-believers. Let's think of all possible events that occur involving two coins. The following table includes the results of two independent tosses.
| Heads (H) | Tails (T) | |
|---|---|---|
| Heads (H) | H H | H T |
| Tails (T) | T H | T T |
| Heads (H) | Tails (T) | |
|---|---|---|
| Heads (H) | H H (25 %) | H T (25 %) |
| Tails (T) | T H (25 %) | T T (25 %) |
Flipping two coins at once can be used to model the response of one person — if at least one of the coins lands on heads, we can count that person as a non-believer. Ghost Non-Believers: & H H, H T, T H Ghost Believers: & T T Modeling the response of five people at once would require flipping each of the two coins a total of five times.
Since we want to simulate a probability, we need to repeat this step some number of times, for example a 100 times. Then the probability of randomly selecting a group of 5 non-believers would be the number of times that all five pairs coins landed on heads at least once, divided by 100.
This time we want to design a simulation that would estimate the probability of randomly selecting 5 non-believers using a calculator. Let's simulate the process event using the random integer generator on our graphing calculator. The numbers 1, 2, and 3 represent a non-believer and 4 represents a believer.
Here, a series of 5 digits that are all at most 3 represents a group of 5 non-believers. If any of the 5 digits is a 4, the group includes at least one believer.
If we were to run this simulation 100 times, dividing the total count of series of numbers that are all at most 3 by 100 would give us an estimate of the probability of all 5 people being non-believers. Since this is a simulation, the result may, and most likely would be, different from the theoretical probability of the event.