forty - four percent of the members of the science club wear blue shirts. which of the following is a…

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

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

Answer

Explanation:

Step1: Recall binomial experiment criteria

A binomial experiment has a fixed - number of trials, each trial has only two possible outcomes (success or 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" has a fixed number of trials ($n = 8$), two outcomes (wearing a blue shirt or not), a constant probability of wearing a blue shirt ($p=0.44$) for each member, and the selection of each member is independent. This is a binomial experiment.
  • Option 2: "Selecting members randomly until one without a blue shirt is chosen" is a geometric experiment as it has a non - fixed number of trials (we stop when a certain event occurs).
  • Option 3: "Selecting members randomly until one with a blue shirt is chosen" is also a geometric experiment as the number of trials is not fixed.

Answer:

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