Question

A barista's friend believes theres no difference in pouring milk in before or after your coffee. His barista friend disagrees. He challenges her by giving her three cups; in two the coffee was poured first, and in the third, the milk was poured first. She must identify the cup into which the milk was poured first. This experiment is repeated a total of 8 times, without feedback. The barista gets it right 6 out of the 8 times. What is the probability that she would have selected the right cup 6 or more times if the friend is right and there is no difference at all in taste?

Answer 1

We use Binomial distribution as :

where,

n = Sample size or Number of trials

p = probability of success

x = Number of success

Let X denote the number of times she would have selected the right cup

In this case,

p = Probability that she gets the right cup = 1/3

n = 8

We need to find :

Note :

So,

Required probability = Probability that she would have selected the right cup 6 or more times = 0.0171+0.0024+0.0002 = 0.0197