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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.'

1 Answer

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Final answer:

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.

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