Question

Which of the following choices can be considered binomial random variables?

1) Flip a fair coin 20 times. Let c be the number of flips that show 'tails.'
2) Flip a fair coin 20 times. Let b be the number of flips that show 'heads.'
3) Flip a fair coin 2 times. Let a be the number of flips that show 'heads.'

Answer 1

The choices that can be considered binomial random variables are flipping a fair coin 20 times and flipping a fair coin 2 times. To be considered a binomial random variable, an experiment must have a fixed number of identical trials with two possible outcomes, and the random variable of interest is the number of successes.

Step-by-step explanation:

The choices that can be considered binomial random variables are:

1. Flip a fair coin 20 times. Let c be the number of flips that show 'tails.'
2. Flip a fair coin 2 times. Let a be the number of flips that show 'heads.'

To determine if a random variable can be considered binomial, it must satisfy the following characteristics:

• The experiment consists of a fixed number of identical trials.
• Each trial has only two possible outcomes, often referred to as success and failure.
• The probability of success is the same for each trial.
• The trials are independent, meaning the outcome of one trial does not affect the outcome of another.
• The random variable of interest is the number of successes in the fixed number of trials.