Chapter 11.4, Problem 9PPS

To determine

Determine whether each experiment is a binomial experiment.

Answer to Problem 9PPS

  $\boxed{\text{NOT a binomial experiment}}$

Explanation of Solution

Given information:

Determine whether each experiment is a binomial experiment or can be reduced to a binomial experiment.

A ball is hidden under one of the hats shown below. A hat is choosen, one at a time, until the ball is found.

Calculation:

Consider that a ball is hidden in one of the sets of $6$ hats on a table.

Consider an experiment:

A person chooses one hat at a time, until the ball is found.

A binomial experiment is an experiment with $n$ number of independent trials and each trial has only two possible outcomes, success or failure. In a trial, the probability of success is $p$ and that of failure is,

  $q=1-p$

Since the probability of getting a ball is changed in each trial that a person performs, the trials are not independent.

Hence, the experiment of a person choosing one hat at a time, until the ball is found is $\boxed{\text{NOT a binomial experiment}}$ .