A coffee shop owner knows from past records that 18 of all c

A coffee shop owner knows from past records that 18% of all customers who enter her store will buy a danish. if 12 people enter the store what is the probability that no one buys a danish?

How many people must enter the store before she is 85% sure that at least one person will buy something?

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    15      
p = the probability of a success =    0.2      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.035184372 [ANSWER]

****************

b)

Note that

P(at least 1) = 1 - P(0) = 0.85

Thus, P(0) must satisfy

P(0) = 0.15.

Using a table of binomial probability values, if P(0) is at most 0.15, we get that

n >= 9. [ANSWER]