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:

A binomial experiment has fixed number of trials, two outcomes (success/failure), independent trials, and constant probability.

• First option: 8 trials (select 8 members), each trial has 2 outcomes (blue or not), independent, p=0.44 constant.
• Second: Records number, not individual trials' outcomes.
• Third/Fourth: Trials until success (no fixed n), so not binomial.

Answer:

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