[kmm23]

A deck of cards is shuffled, and I choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and I again choose a card at random, observe its color, and replace it in the set. This process is repeated until I get a red card with X denoting the number of draws required. The random variable X has which of the following probability distributions?

A. The normal distribution, with mean 26 and variance 13
B. The binomial distribution, with parameters n = 52 and p = 0.5
C. The binomial distribution, with parameters n = 26 and p = 0.5
D. None of the answers is correct

[Celine91]

This is a geometric distribution (experiment performed repeatedly until particular outcome is observed). A sequence of independent Bernoulli trials, each with probability of success p, and X number of the first trial at which a success is recorded. P(X = n) = (1-p)^n-1 * p

so answer is none of the above.