A bowl contains six marbles of which two are green and four are red. The marbles are removed one by one, at random and without replacement. Let X be the number of the drawing at which a red marble is removed for the first time. Find the probability function of X, and E(X)

Alonzo Odom

Alonzo Odom

Answered question

2022-07-20

Find probability function and E(X)
A bowl contains six marbles of which two are green and four are red. The marbles are removed one by one, at random and without replacement. Let X be the number of the drawing at which a red marble is removed for the first time. Find the probability function of X, and E ( X ).
For the probability function, I believe that this question is a geometric distribution, so I have P [ X = x ] = p q x 1
For E ( X ) = 1 / p since it's geometric distribution
Is it the Hypergeometric distribution?
So E ( Y ) = n r / N

Answer & Explanation

suponeriq

suponeriq

Beginner2022-07-21Added 10 answers

Step 1
No, you are not correct; for a geometric distribution, you have to have the same probability of "success" on each draw, whereas here the probability of getting a red depends on the marbles that have been drawn so far.
Step 2
For instance: the probability that you first get a red marble on the second draw is precisely the probability of getting a green first and then a red, which is 2 6 4 5

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