By definition, a binomial experiment is an experiment that satisfies these four conditions:
0. A fixed number of trials,
,
1. Each trial is independent of the others,
,
2. There are only two outcomes,
,
3. The probability of each outcome remains constant from trial to trial.
We analyze which of the statement satisfies the four conditions.
1) "Drawing a single marble from a jar that has 4 red marbles and 6 black marbles until you get a red marble".
This experiment does not satisfy conditions 2 and 4:
• each trial dependent on the others,
,
• the probability does not remain constant.
2) "Asking 50 people how tall they are and recording their heights".
This experiment does not satisfy condition 3:
• there is only one outcome for each trial.
3) "Flipping a coin until it lands with tails showing".
This experiment satisfies the four conditions.
4) "Rolling a number cube 30 times and recording the number of times a 6 is rolled".
This experiment does not satisfy condition 3:
• there are six possible results in each trial.
Answer
The third experiment, "fipping a coin until it lands with tails showing", is a binomial experiment because it satisfies the four conditions.