Question

which of the following is a binomial experiment?
○ flipping a coin until it comes up tails
○ flipping a coin until 8 heads are recorded
● flipping a coin 10 times and recording if it comes up heads
○ flipping a coin by 10 different people and recording the age of each person

Explanation:

Step1: Recall Binomial Experiment Criteria

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

Step2: Analyze Each Option

• Option 1: Flipping until tails (number of trials not fixed) → Not binomial.
• Option 2: Flipping until 8 heads (number of trials not fixed) → Not binomial.
• Option 3: Flipping 10 times (fixed trials), independent, 2 outcomes (heads/tails), \( P(\text{heads}) = 0.5 \) constant → Binomial.
• Option 4: Recording age (not related to coin flip outcomes) → Not binomial.

Answer:

Flipping a coin 10 times and recording if it comes up heads