Question

forty - four percent of the members of the science club wear blue shirts. which of the following is a binomial experiment? selecting eight members randomly and recording whether each member is wearing a blue shirt selecting eight members randomly and recording the number in the group wearing a blue shirt selecting members randomly until one without a blue shirt is chosen selecting members randomly until one with a blue shirt is chosen

Explanation:

Step1: Define binomial experiment

A binomial experiment has a fixed number of trials, each trial has only two possible outcomes (success - failure), the probability of success is constant for each trial, and the trials are independent.

Step2: Analyze each option

• Option 1: Selecting eight members randomly and recording whether each member is wearing a blue shirt. There are a fixed number of trials ($n = 8$), each trial has two outcomes (wearing blue shirt - not wearing blue shirt), probability of wearing a blue shirt is $p=0.44$ (constant) and trials are independent. This is a binomial experiment.
• Option 2: Selecting eight members randomly and recording the number in the group wearing a blue shirt. This is a binomial - related situation but it is more about the result of a binomial experiment (finding the number of successes in $n$ trials) rather than the binomial experiment itself.
• Option 3: Selecting members randomly until one without a blue shirt is chosen. This is a geometric experiment (number of trials until first success where success is finding a non - blue - shirted member).
• Option 4: Selecting members randomly until one with a blue shirt is chosen. This is a geometric experiment (number of trials until first success where success is finding a blue - shirted member).

Answer:

Selecting eight members randomly and recording whether each member is wearing a blue shirt