Question

On average, the probability of customers at a local AMC theater adding candy to their purchase is 0.30. What is the probability that the first person to add candy will be before customer 1? Round you answer to 2 decimal places.

Answer 1

Here we take a customer adding candy to his purchase as success

Probability of success p = 0.30

So failure is not adding candy to his purchase by a customer = q= 0.70

We need to find the probability X number of of succes before the first customer

So we can say that X follows a negative bionomial distribution

For a negative bionomial distribution

x denote the number of trials required to produce r success here x=0 as before customer 1 so number of trial x= 0

r is the number of success here r = 1 we need 1 success

p = 0.30 and q=0.70

Now the negative bionomial b(x,r,p)= x+r-1Cr-1()=1-1C1-1(0.30).(0.70)

=1x.30x1/0.70(poer -1 means devided by )

=0.30/0.70=0.4285=0.43