Question

Six customers enter a three-floor restaurant. Each customer decides on which floor to have dinner. Assume that the decisions of different customers are independent, and that for each customer, each floor is equally likely. Find the probability that exactly one customer dines on the first floor.

Answer 1

Answer:

The probability that exactly one customer dines on the first floor is:

                     0.26337  

Step-by-step explanation:

We need to use the binomial theorem to find the probability.

The probability of k success in n experiments is given by:

       $P(X=k)=n_C_k\cdot p^k\cdot (1-p)^{n-k}$

where p is the probability of success.

Here p=1/3

( It represents the probability of choosing first floor)

k=1 ( since only one customer has to chose first floor)

n=6 since there are a total of 6 customers.

This means that:

$P(X=1)=6_C_1\times (\dfrac{1}{3})^1\times (1-\dfrac{1}{3})^{6-1}\\\\\\P(X=1)=6\times (\dfrac{1}{3})\times (\dfrac{2}{3})^5\\\\\\P(X=1)=0.26337$