Question

Determine whether the following are binomial experiments. If not, explain which requirement is violated. If so, state the distribution of the random variable in the scenario.

A) Bob is playing a game at a carnival where he gets to play until he loses. The probability that he wins the game is 0.25. Assume he does not get better each better each time he plays. Let X count the number of games that Bob wins.

B) Charlie flips a coin three times. The probability if seeing a head on each flip is 0.5. Let X count the number of times out of three flips that we observe a head.

C) A group of 50 movie critics are reviewing a new take on an old classic movie using a 5-star scale (more stars=better review). Let the random variable X count the number of stars out of five that each critic gives

Answer 1

Conditions for Binomial experiment,

1. Trails must be independent from each other.
2. Each trial must have only two possible outcomes.
3. The probability of success must remain same from one trial to other.

A)

At each trial the probability of winning remains same. The number of trials are not fix. That is number of trials depend upon the chances he need to loose. So it is not a binomial experiment.

B)

Here probability of getting head remain same at each trial. Number of trials are fixed to three. There are only two outcomes for each trial: head or tail

So it is a binomial experiment with parameters n=3 and p=0.5.

C)

There are more than two possible outcomes for each trial. The outcomes can be 1, 2, 3, 4 or 5 stars.

So it is not a binomial experiment.