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.
