Final answer:
The correct distribution describing the number of trials until a heads appears when flipping a coin is geometric. However, among the given options, the closest is the binomial distribution because it can sometimes be considered a special case of the binomial when focused on the number of trials until the first success. Option C is the nearest correct answer.
Step-by-step explanation:
The student wants to know the distribution of X, which represents the number of trials until Adam, Beth, or John gets a heads when flipping a coin. The conditions given for the distribution of X and the examples provided in the question hint toward the geometric distribution.
A geometric experiment has three major characteristics: it consists of Bernoulli trials, there is no upper limit to the number of trials, and the probability of success (or failure) is the same for each trial. Since flipping a coin until getting a heads fits these conditions, the correct answer is the geometric distribution, which isn’t listed as one of the options a) Normal, b) Exponential, c) Binomial, d) Poisson.
However, a geometric distribution is sometimes considered a special case of the binomial distribution, where the number of trials is not fixed, but we are instead interested in the number of trials up to the first success, so the closest appropriate option provided would be binomial.