Probability Question

Question

1. Your local sandwich store knows that 70% of its customers choose chicken sandwiches; the rest choose ham.
2. What is the probability of selling 2 chicken sandwiches from the next 3 customers? You may need to draw a tree diagram to assist you.
3. Suppose that everyday, they have 120 customers. On average, how many chicken sandwiches do they sell daily?

Answer 1

Prefer to do this as a binomial expansion of (c+h)^3 where c =chicken and h=ham

this is c^3 +3c^2h + 3ch^2 + h^3

we would be interested in the c^2h term which represents precisely 2 chicken and 1 ham sandwich

this is 3(.7)^(.3)= .441

part 2 is (120)(.7)= 84 chicken sandwiches