At a certain breakfast restaurant, the probability of a customer ordering coffee is 0.8. When the restaurant seats two new customers, X is the number of customers ordering coffee.
What is P(X=0)?
Enter your answer, as a decimal, in the box.
P(X=0)
how can i solve this ?
Assuming P(X=0) means neither ordered coffee = (1-.8)(1-.8) = ?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
To solve this problem, you can use the concept of probability. In this scenario, the probability of a customer ordering coffee is given as 0.8.
To find the probability of zero customers ordering coffee (P(X=0)), you need to identify the total number of possible outcomes when seating two new customers and calculate how many of those outcomes have zero customers ordering coffee.
The number of possible outcomes when seating two customers is determined through the concept of combinations. When seating two customers, the possible outcomes for their coffee orders are as follows:
- Both customers order coffee
- Only the first customer orders coffee
- Only the second customer orders coffee
- Neither customer orders coffee
Since the probability of a customer ordering coffee is 0.8, the probability of a customer not ordering coffee is 1 - 0.8 = 0.2.
Now, calculate the probability of zero customers ordering coffee by considering the last possible outcome: neither customer orders coffee. This outcome occurs when the first and second customers both do not order coffee.
Therefore, the probability of zero customers ordering coffee (P(X=0)) is equal to the probability of neither customer ordering coffee, given by P(neither customer orders coffee) = P(first customer does not order coffee) * P(second customer does not order coffee) = 0.2 * 0.2 = 0.04.
In the given problem, the answer to P(X=0) is 0.04.