A survey showed that 72 % of people in USA like pizza. We are asked to find the probability that 3 randomly selected people like pizza. Events such as asking random people if they like pizza are independent. Let's recall the formula for the probability of independent events.
Independent Events
If two events A and B are independent, then the following statement is true.
P(AandB)=P(A)* P(B)
Let's say that P(Pizza) is the probability that a random person in the USA likes pizza. Then, the probability that 3 randomly selected people like pizza is P(Pizza, Pizza, Pizza). Now, we can use the probability formula for independent events.
P(Pizza, Pizza, Pizza)= P(Pizza)* P(Pizza)* P(Pizza)
We know from the survey that P(Pizza) is equal to 72 %, which can be also written as 0.72. Let's substitute that into our equation.
P(Pizza, Pizza, Pizza)= 0.72* 0.72* 0.72
≈ 0.37
The probability that 3 randomly selected people like pizza is about 0.37, or 37 %.
