Question

Suppose the five cards are drawn from a deck, one at a time, without replacement. Let X=the number of times an ace is drawn from this experiment. What are the possible values of X? What kind of random variable does this represent?​

Answer 1

According to the information given, it is found that X is an hypergeometric variable, that can assume values between 0 and 4.

The cards are drawn without replacement, hence trials are dependent and X is an hypergeometric variable.

What is the hypergeometric distribution formula?

The formula is:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.

• N is the size of the population.

• n is the size of the sample.

• k is the total number of desired outcomes.

In a standard deck, there are 4 Ace cards, hence $k = 4$ and X assumes values between 0 and 4.

You can learn more about the hypergeometric distribution at https://brainly.com/question/4818951