A test for extrasensory perception ESP involves asking a per

A test for extrasensory perception (ESP) involves asking a person to tell which of 5 shapes-a circle star, triangle, diamond, or heart-appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5 shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first 4 Shapes incorrectly but gets the fifth correct?

Solution

this is a geometric distribution with formula c)

(4/5) ^4 * 1/5