Probability drawing marbles out of a bag without replacement?

Question

I draw three marbles from a bag containing 6 red marbles, 10 blue marbles and 14 green marbles, all indistinguishable except for their colour. The marbles are drawn WITH replacement, and the bag is properly shaken after each marble is returned. Let X be the number of green marbles I obtain. Does X have a Binomial distribution?

a. No, because there are three, not two, categories of results.

b. Yes

c. No, because the selections of marbles are not independent

d. No, because the prob of a green marble changes from draw to draw

e. No, because the number of trials is not fixed

I have eliminated a and c. I am thinking the answer is b. can somebody help me out. Thanks

Answer 1

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Yes (b)

Because the drawn marble can be given the result of success (green marble) and fail (any of the others)

Answer 2

The following conditions for using Binomial distribution are fulfilled.

a) An experiment is to be performed for a fixed number of trials n = 3

b)In each trial there must be two possible outcomes success is drawing a GREEN Marble and failure is Non-green marble

c) The probability of a success should remain constant from trial to trial p = 14C1/30C1 remained constant.

d) The trials are statistically independent because of replacement of the marble drawn

Therefore answer to the question is (b)

You are correct

The random variable X have a Binomial distribution