a 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 : Ghost Believers : 75 % 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

Each of these events is equally likely, with a probability of $25 % .$ Then, any three of these events occurring has a probability of $25 + 25 + 25 = 75 %$ chance of occurring. For example, the probability of getting heads at least once is $75 % .$

	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 : Ghost Believers : H H, H T, T H 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 $100 .$

Exercise