Which of the following is an example of a binomial random variable?

• A. The number of heads obtained when flipping a fair coin $10$ times
• B. The time it takes for a student to finish an exam
• C. The weight of apples in a basket
• D. The number of cars passing through an intersection in $1$ hour

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the definition of a binomial random variable. A binomial random variable counts the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant across trials.
2. Step 2: Analyze each option to see if it fits the binomial criteria: fixed number of trials, two possible outcomes per trial, independence, and constant probability.
3. Step 3: For 'The number of heads obtained when flipping a fair coin 10 times': There are 10 fixed trials (coin flips), each with two outcomes (head or tail), independent flips, and a constant probability of heads (0.5). This matches the binomial setup.
4. Step 4: For 'The time it takes for a student to finish an exam': This is a continuous measurement, not counting successes in trials, so it is not binomial.
5. Step 5: For 'The weight of apples in a basket' and 'The number of cars passing through an intersection in one hour': Both are not counting successes in fixed trials with two outcomes; weight is continuous, and cars passing is a count but not from fixed trials with two outcomes, so neither is binomial.